## Thursday, 6 July 2017

### [Homework] 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

1. Raj and Michael decided to race to the Redhill and Greenfield respectively. Raj started sprinting from Greenfield and Michael started running from Redhill at the same time(0800). At 0900, Raj started jogging as he was tired. Also at 0900, Michael took a break so as to regain energy to sprint all the way to Greenfield at 0930. At 0945, Raj took a break until 1030 before sprinting to Redhill.

2. Micheal lives in Redhill. One day, he suddenly decided to visit his cousin Raj, who lived in Greenfield. He set off at 8am and took the MRT, which moved at a speed of 1km/h. At 9am, however, the MRT broke down and Micheal was stranded at a station. After half an hour, the train was still out of order and Micheal grew impatient. He decided to take a taxi instead of waiting. The taxi travelled at a much faster speed of 4km/h, so Micheal was able to reach Raj's house Greenfield by 11am. However, Raj was not at home. This was because...

On that same day, Raj decided to surprise his cousin Micheal who lived in Redhill. From 8am to 9am, he cycled towards Redhill at a speed of 3km/h. After one hour, he grew tired and reduced his speed. After 45 minutes, Raj spotted a squirrel on a tree branch. He dismounted and tried climbing the tree to catch the squirrel. He was unsuccessful after 45 minutes of climbing. He was so exhausted that he dumped his bike and took a bus the rest of the way to Redhill. He finally reached Micheal's house at 11.30am. However, Micheal was not at home!

What a mess.

The end of story :)

3. After a long day of work (Night Shift) at Greenfield, he drove his car for 1 hour, and travelling 3km away from Greenfield. However, the car broke down and stopped in the middle of a park filled with bikes. Then, he rented an oBike. But first, he wasted data through downloading the oBike application. He rode the oBike for 1km before stopping for street food. After munching for 45 minutes, he decided to book an Uber cab. However, he wasted more data downloading the Uber application. When he reached his house at Redhill. Once he got home, he realised how much data he wasted and that he had to pay \$50 for the data bills. He then fell onto the floor and went into a deep slumber.

Michael rented an oFo from Redhill and rode 1km in 1h. Then, he stopped for a 30min breakfast before stealing a Porsche and driving it for 6km in 1.5h to reach the newly opened park at Greenfield. However, as soon as he got off the car, he was caught by the police.

4. On a Sunday, Michael decided to Greenfield to do some Christmas shopping. He left his home at Redhill at 8am, and took a long leisurely walk around Redhill neighbourhood at 1km/h before proceeding to Redhill MRT station to catch the train to Greenfield.
However, when Michael reached Redhill MRT station, he realised there was a train disruption due to a track fault, and decided to take the bus while waiting at the bus stop, as an alternative route. He saw a cafe at the MRT station, and decided to grab a bite before going to the bus stop. As Michael was a slow eater, it cost him 30min.
Peter, Michael's friend, was driving past the bus stop and saw Michael. Peter decided to give Michael a car ride to Greenfield. However, the traffic was very heavy on the way to Greenfield, so the car travelled a distance of 6km/h, and it look an hour to reach Greenfield. In the end, Michael and Peter had a fun time doing window shopping around Greenfield.

Also on Sunday, Raj made his way Redhill to collect a Christmas present for his mother. He left his house exactly at 8am, and drove at a a speed of 3km/hour due to an accident on the expressway, leading to heavy traffic. After an hour, he drove at a much slower speed of about 1.3km/h, as the traffic condition got even worse.
To make things even worse, after 45min, one of the car tyres burst and he spent another 45min to replace the tyre, as he had a spare tyre in the car. After replacing his tyre, he started to drive his car again at 3km/h, as traffic conditions got much better. After an hour, he finally reached Redhill, collected the Christmas present, and began the boring journey back home.

5. Michael was in Redhill when he started to walk towards Greenfield. He walked 1km in 1h. Next, he was very tired so he decided to stop and eat a late breakfast. Later, he took a bicycle and started cycling at full speed till he reached Greenfield.

After a jog at Greenfield, Raj took the MRT. When he reached the MRT station at 0900, he rented a bicycle and he rode to a food court for a snack. After that, he rode with the bicycle back to Redhill.

6. One day, Michael got a new pet dog. He decided to visit his friend, Raj, so that his new dog could play with Raj's dog. He started his journey at 0800hr and on his way to Raj's house, his dog was moving very slowly at a speed of 1km per hour because it was very tired. After 1 hour of travelling, Raj decided to give his dog a break and bought some doggy treats for it. After 30 minutes, his dog became active so he walked it for another 1 hour 30 minutes at a speed of 4km per hour until he reached Raj's house. But when he reached there at 1100hr, Raj wasn't home.

Apparently, Raj did not have a phone, so Michael messaged Raj's brother that he would be coming to his house to play with Raj's dog. But his brother tricked him by telling Raj that Michael wants him to go to his house with his dog.

After Raj's brother tricked Raj by telling him that Michael wants him to go to his house with his dog, Raj left home at 0800hr with his dog to go to Michael's house. He walked his dog for an hour at a speed of 3km per hour. His dog started to slow down after that so he took a break. After the break, he started walking it again for another hour at the same speed of 3km per hour. After a long journey, he finally reached Michael's home at 1130hr. But he was surprised that Michael wasn't home. Michael's mother told Raj that Michael had actually gone to his house.

Raj then called Michael using Michael's home phone and they were discussing about what had happened. After about 5 minutes of discussing, they found out that Raj's brother tricked Raj and were angry at him. So, they started to plan a trickery to teach him a lesson...

7. It was Michaels’s birthday and Raj decided to give him a surprise visit! Raj lived at Greenfield while Michael lived at Redhill. Raj took a MRT which travelled at 3km/h at 8 am. At 9 am, The MRT train broke down so he had no choice but to take the bus which travelled at a slower rate. At 9.45 am, he stopped by a mall and decided to shop for a present for Michael. After 45 minutes, he settled on a pepperoni pizza and a Star Wars Bobble Head figurine. Lastly, he took another train which travelled at 3km/h. Upon reaching Michaels's house at 11.30 am, Raj realised that Michael was not home! He checked his phone and realised that Michael had actually went to his house spend the day together with him…

That morning, Michael left his house at 8 am and rented an oBike. He cycled towards Greenfield at a speed of 1km/h. After 1h, he stopped by a coffee shop to have his breakfast. At 9.30 am, he flagged a taxi which travelled at 4km/h and travelled all the way to Raj’s house. He reached Raj’s house at 11 am.

8. Michael works as a post officer. As it was another ordinary weekday, he decided ride his bicycle to the post office. He started at 0800 and rode at a speed of 1km/h. He reached the post office at 0900. He took 30 minutes to transfer all the letters from the office into the bicycle. Next he travels to Greenfield at 0930, at a speed of 2.4 km/h.

On the opposite, Raj, who just completed his night shift work at 0800, decided to go for a run back home. For the first one hour, he ran at a speed of 3 km/h, before slowing down to jog at a speed of 0.7km/h. After that, at 0942 to 1000, he decides to rest at a coffee shop for a cup of Kopi'o and kaya toast. At around 1030, his good friend Michael cycled past him and they both exchanged pleasantries. However, Michael did not stop because he was in a rush.

Michael continued his way to Greenfield and reached Greenfield at 1100.

Raj felt quite full, so he decided to ride an oBike home at Redhill. He rode at a constant speed of 4km/h and reached home at 1130.

The end.

9. One boring morning, at 0800, Raj decided to go to Redhill for breakfast. Michael also decided to go to Greenfield for breakfast at 0800. Raj wasted no time and sprinted 3km towards Redhill from 0800 - 0900. However, he got tired and decided to start jogging at 0900. Michael decided to sprint towards Greenfield from 0800 - 0900. However, at 0900, he stopped for some ice-cream from 0900-0930. At 0942, Raj saw a snack stand and decided to have some snacks there. Ymm, yum! After having his ice-cream, Michael started sprinting to Greenfield from 0930 all the way to 1100 in which he reached Greenfield. After finishing his snacks at 1030, Raj decided to sprint all the way to Redhill and reached there at 1130. They both had their wonderful breakfasts there.

This is just messed up people. I don't even know if its correct. Awkward...

10. Today was the soccer match between SST and LST secondary school. Both Raj and Michael were supposed to report at Dover MRT, however they messed up the locations. Raj, who lived in Greenfield, thought that Redhill was the meeting point while Michael, who lived in Redhill, thought that Greenfield was the meeting point. The distance between Redhill and Greenfield is 7km.

At 0800, Raj, looking at his watch and thinking that he was already late for the soccer match, sprinted at a speed of 3km/h towards Redhill. However, at 0900, he crossed by a huge market where there were a lot of people buying items and hence, had to slowly make his way through the crowd. He also got a bit lost while in the market and thus only walked for 1km from 0900 to 0945 towards Redhill. At 0945, he looked at his watch again and realised that he had worn his watch the other way around. Turning it the correct way, he found out that he was actually quite early for the soccer match. Tired and irritated, he sat on a bench and soon fell asleep for about 45 minutes. At 1030, he woke up and when he realised that he was really late for his soccer match then, he bolted towards Redhill at a speed of 3km/h. He reached Redhill at 1130.

At 0800, Michael, tired and with half-opened eyes, trudged towards Greenfield at a speed of 1km/h. He then went to 7-eleven and bought a bottle of milk tea to perk him up at 0900. For 30 minutes, he chugged down bottles of milk tea while standing by the roadside. At 0930, after chugging down the last bottle of milk tea, he was really hyper and felt as if he was going to participate in the 100 metre sprint. He started to sprint towards Greenfield at a speed of 4km/h for 45 minutes. He reached Greenfield at 1100.

At the end of the day, both Raj and Michael did not manage to attend the soccer match. In addition, they got a message from the soccer coach saying that they were kicked out of the soccer team.