## Tuesday, 15 April 2014

### Lines tell stories

The diagram shows a distance-time graph.
Study the graph carefully, paying attention to the slopes (i.e. the speed), the pauses, the time taken and the distance.

Write a story that takes into account the 'movement' of Raj and Michael.
• It should include information like where they begin their journey.
• It should also take into account the distance they travel, the speed they travel at, what happened during the pauses, etc.

adapted from New Syllabus Mathematics (7th edition) p171

After note: posted on 17 April 2014
Below are some 'factual' information that we can draw from the graphs which can be taken into consideration when composing the story :)

1. Here is my story
Redhill and Greenfield were exactly seven kilometres apart. The two friends which were at loggerheads, lived in these estates. The first one is Raj, living in Greenfield while the second is Michael, who lives in Redhill.
They had a meet-up at Macdonalds, on accident. Raj wanted to go to Redhill to purchase the latest iPhone 6 while Michael wanted to attend tuition in Greenfield.
Raj was walking peacefully till a group of ominous and daunting clouds started to shadow the light, casting darkness below. Lightning struck and but Raj did not bring an umbrella ,so he had to run. Much to his relief, he found a deserted Macdonalds which was actually in service. With his heart pumping, he ran to the store at the speed of lightning, bolting across the raindrops trying to pelt him in their wet embrace.
Michael, on the other hand, brought an umbrella. Unfortunately, luck crushed hard on him as all his tuition resources came out, flopping all over the floor. Realising that he was going to be late for his tuition, he sprinted to Greenland. Suddenly, Raj came running out, eager to get his new iPhone 6. Michael then had an idea to make Raj payback for what he had done to ruin his school reputation. He continued running, and started raising his fist of titanium, preparing to get Raj smashed.
3 seconds
2 seconds
1 second
Before Raj knew it, he was lying on the floor, with Michael dashing past him, leaving debris in his face, which from a vibrant white, had turned into a ashen grey. Michael mocked Raj as he dashed off at the same speed to prevent getting caught.
Raj picked himself up, his head feeling dizzy as he tried to pull himself together. It was just too much. The blow just had too much impact.
When Raj was done walking in circles and falling, he finally started walking at the same way as before, without the cheerfulness, to get his iPhone 6.

2. Mine's a bit nerdy and lame...
But here it goes...

Raj started his journey in Greenfield, while Michael started his in Redhill. Both started at 0800hrs. At 0900hrs, Michael travelled 1km at 1km/h, while Raj travelled 3km at 3km/h. Raj travelled for 1km and his speed remained constant at 0945hrs while Michael’s speed remained constant for 30 minutes from 0900hrs to 0930hrs. He then travelled 2km for 30 minutes at an average speed of 4km/h. They both met each other at exactly 1000hrs. Raj’s speed remain constant until 1030hrs. Raj travelled 3km for 1 hour until 1130hrs, which he has reached Redhill at an average speed of 3km/h, while Michael travelled 4km for 1 hour until 1100hrs and reaches Greenfield at an average speed of 4km/h.

3. Here is mine. I split it into 2 parts, one for Michael and the other for Raj.

Michael: Michael woke up and decided to walk from his house in Redhill to Greenfield. He left his house at 8 a.m., walking at a speed of 1km/h for an hour, covering a distance of 1km. He stopped by a coffee shop at 9 a.m. to have breakfast for half an hour. Then at 9.30 a.m., he continued walking at a speed of 4km/h for 1.5 hours to reach Greenfield, covering 6km more and reached Greenfield at 11 a.m. in 3 hours.

Raj: Raj woke up and decided to walk from his house in Greenfield to Redhill. He left his house at 8 a.m., walking at a speed of 3km/h for an hour, covering a distance of 3 km. Soon, he felt tired and decided to slow down his pace at 9 a.m., walking at a speed of 1 1/3km/h for 45 minutes, coving another 1km. At 9.45 a.m., he stopped at a food court to have breakfast for 45 minutes, seeing Michael walk past the food court at 10 a.m. At 10.30 a.m., he continued walking at a speed of 3km/h for 1 hour to reach Redhill, covering 3km more and reached Greenfield at 11.30 a.m. in 3.5 hours.

4. Raj and Michael are travelling 7 km between Redhill and Greenfield starting at 08 00 hours. Raj starts from Greenfield whereas Michael starts from Redhill. Michael travels a distance of 1 km, taking 1 hour (speed:1km/h). Then, he stops for 30 mins after which, he travels 6 km in 1.5 hours (speed:4km/h). Raj first travels 3 km taking 1 hour (speed:3km/h). He then covers the next 1 km in 42 minutes (speed:1.4km/h). After that, he stops for 48 minutes and covers the balance 3 km in 1 hour (speed:3km/h).

5. Raj wanted to go to Redhill, and Michael wanted to go to Greenfield. They started from Greenfield and Redhill at 0800 respectively. Greenfield and Redhill is 7km away from each other. At first, Raj travelled at 3km/h, until 0900, when he slowed down, reaching 4km into his journey at 0942. He rested for 48 minutes before continuing at 3km/h, until he reached Redhill at 1200 hours. Michael started at 1km/h, until 0900, where he rested for hald an hour, before continuing the last 6km at 4km/h, reaching Greenfield at 1100.

6. Raj started his journey from Greenhill, while Michael started from Redhill. From 8 to 9 am Raj walked 3km closer to Redhill while Michael walked 1km closer to Greenhill. From 9am to 9.30 am, Michael took a break, while from 9am to 9.42 am Raj walked 1km closer to Redhill. After taking a break, Michael walked for one and a half hour to reach Greenhill. Raj took a break from 9.42 am to 10.30 am. He then continued to walk for another 1 hour to reach Redhill.

7. Raj and Michael,2 friends.Raj lived in Greenfield whereas Michael lived in Redhill. They decided to see how much time they took going towards each of their states.They both started their trip at 0800.

Raj was going to Greenfield as he wanted to attend a show by his favourite band.Raj started his journey from Greenfield at 0800(Greenfiled time).Raj covered 3km in the first hour of his journey as after 3km.In the next 45 mins,he traveled a kilometre.He took 25mins more to complete one kilometre than a kilometre in the first hour.After covering a distance of 4km he decided to take a rest in a nearby inn where after 15 mins he saw his friend,Michael, run past the inn.After 30 more mins of rest,he made a move and started walking towards the concert place.He reached Greenfield at 1130.His average speed for the whole journey was 2km/h.

Michael was going to Redhill to his grandparents' house.He covered 1km in the first hour and rested for 30 mins before carrying on.The next 1/1/2 hours,he jogged to his grandparents' house.At 11 00,he reached his grandparents' house.His average speed was 7/2km/h.

They concluded that Michael was faster as his speed was 7/2km/h whereas Raj's speed was 2km/h.So in an hour Michael covered a greater distance than Raj,thus he reached his destination faster.

8. Raj decided to meet his friend, Michael, who lives at Redhill. Meanwhile, Michael also planned to visit Raj who lives at Greenfield. Michael started his journey at 08 00 and so does Raj. After walking for one hour, Michael stopped at 7 eleven to buy a drink. Half an hour later, he continued his journey. It was 09 30, Michael started running, he was going to be late for tuition which was just beside Raj's house. Raj had no idea that Michael was going to visit him before tuition, so he also went to look for Michael. He assumes that Michael was still packing his tuition bag and is still home. He ran for one hour and was tired, so he slowed down for a while and took a break. At 10 00, Michael past by the bench where Raj was resting, but they did not see each other. At 10 30, Raj continued his journey. Michael was travelling at an average speed of 2 1/3km/h and Raj was travelling at an average speed of 2km/h. When they reached their destination, they did not see each other. They called each other.

9. Raj was going to kill michael. Micheal was scared so he ran away from his house at redhilll to greenhill to hide, forgetting that Raj lives at redhill. Raj ran towards redhill at a fast pace while Micheal jogged as a slower pace. however, at 9am, Raj tired down and ran slower. Micheal saw Raj with his binoculars and hid. At 9.45, Raj realised that he forgot to bring his knife and bought one. Raj had an argument with the knife vendor an micheal ran away scott free! He hid at greenhill till marssions kidnapped him.

10. Michael went window shopping with his friend at 8am, walking towards Greenfield in a constant speed for an hour, by then he travelled 1km. After getting all the necessities, he proceeded on to McDonalds to rest there for half an hour.
At the same time, somewhere else in Greenfield, at 8am, Raj was brisk walking towards an MRT station on his way to Redhill. He kept up his pace for an hour before slowing down because he got tired. Then at 0945, he decided to take a break at McDonalds for 45 min. By then he was 4km away from Greenfield and 3km away from Redhill. At 10:30 he proceeded to brisk walk at the same pace as the beginning, 3km per hour. After an hour of walking, he finally reached his final destination. It took him three and a half hours in total.
A few hours ago, Michael who was still at McDonalds relaxing, waited till the clock struck 0930 before getting up to walk at a constant speed of 2 1/3 km per hour for 3 hours and then finally reaching his destination at 11 o'clock, 1 hour before Raj.

11. Raj was a tourist to Singapore and had decided to adventure Singapore a bit on his own as he had nothing on that day. Michael had an important meeting on the same exact day and was rushing to office. Michael’s office was in Greenfield while Raj lived there. Michael left for work on his cycle at 8 a.m. and so did Raj for sight seeing.

Michael was stuck in a traffic jam for an hour and was slowed down and travelled only 1 km. In the middle of the traffic jam, he stopped at McDonalds to have a snack as he was frustrated that he was barely inching forward and since he had not had eaten his breakfast, he thought it was a good idea to stop by. After having his meal for half an hour, he continued his journey and realised that he was no longer stuck in traffic and he drove on and reached office in 1.5 Hours at a speed of 4 kilometres per hour.

As for Raj, he left Greenfield and rode on for 3 kilometres in 1 hour but soon slowed down to 1 kilometre in 45 minutes. He went to Pizza Hut on the way and gobbled a large pizza in 45 minutes. He then had a fast drive to his destination, Redhill, in 1 hour at 4 kilometres in an hour.

12. Raj and Michael were planning to surprise each other at each other’s homes since they shared the same birthday and their birthday was on that day. Michael lived at Redhill and Raj lived at Greenfield. Both of them left home at 0800. They both started making their way to each other’s home. However, at 0900, Michael realised that he had forgotten to bring Raj’s present with him. And so, he asked his friend to go to his house, get the present, and bring it to him. However, Michael’s friend only reached Michael at 0930. Soon after 0930, Raj also realised that he had left Michael’s present at home. And so, Raj did the same thing and asked his friend to get the present from his house and bring it to him. However, Raj’s friend only reached him at 1030. They both decided that they might be late. And so, both of them rushed to each other’s house only to realised that the other party wasn’t at home.

13. Michael starts his journey from Redhill to Greenfield to meet his colleagues at 0800. He then travels at 1km/h for the first hour. Michael became hungry and stopped to eat. He then continued to travel the remaining 6 km in 1 1/2 hours and reaches his destination, Greenfield at 1100, and starts to chat with his colleagues.

Raj starts from Greenfield on his way to his church in Redhill at 0800. He travels at an average speed of 3km/h for the first hour.
Raj meets a friend he has not contacted for many years and stops to chat. After that he then takes another hour to travel the remainder 3 km and has reached his church.