Between now and October (if we do go ahead with the PSLE route), I'll need to figure out how to help Brian present his math working for Speed questions better. Trouble is I'm pretty bad at Speed questions myself.
The working he's done here is entirely self-concocted, he hasn't learnt this in school, I've not taught him any particular method cos I don't really know how to present answers for Speed questions either and obviously, he is not following the model method taught in Singapore assessment books.
The thing is he gets the answers right, it's just the working that needs refining, and some discipline on his part not to skip steps. Anyone else finds his working confusing? I've included his verbal explanation in Italic, but look at his working without reading his explanation and let me know how many marks he'd lose even if he gets the answer right, assuming each question is 5 marks. Suggestions for improvement, with method mostly intact, would be much appreciated.
1. Fandi took 3h to travel from town A to town B. On the way, he passed a motorcyclist who was travelling in the opposite direction at a uniform speed of 48km/h. 1 and 3/4 h later, Fandi reached town B while the motorcyclist was still 6km away from town A. Find the distance between the two towns.
Distance between meeting point and Town A
= (48 x 1 3/4) + 6
= 84 + 6
= 90km/ 5/4h
Distance between both towns
= 72km/h x 3h
Brian: The motorcyclist took 1 and 3/4 of an hour to travel from their meeting point to a point 6km away from Town A. So the distance between their meeting point and Town A is the motorcyclist's speed times 1 3/4h plus 6 which equals 90. 90km is also the distance that Fandi travelled from Town A to the meeting point. He took 1 and 1/4 of an hour to travel to the meeting point, so his speed is 90km per 5/4 of an hour, which equals 72km/h. He took 3 hours to travel from Town A to Town B, so the distance between the two towns is 72 x 3 = 216.
2. Richard left town A for town B at 10am. 3/4h later, Linus left town A for town B and overtook Richard at 1230pm. Linus arrived at town B at 105pm. At what time did Richard reach town B?
Let Richard's speed and Linus's speed be R and L respectively.
2 1/2 R = 1 3/4 L
5/2 R = 7/4 L
20 R = 14 L
L = 10/7 R
7/3 L = 10/3 R
Richard took 10/3 hours to reach Town B.
Richard reached Town B at 120pm.
Brian: If you put it algebraically, you're only given one piece of information which is 2 1/2 R = 1 3/4 L (2 1/2 and 1 3/4 are the number of hours R & L travelled respectively when they met) so all you can do is compare the two variables. Since Linus took 2 and 1/3 hours (or 7/3 h) to reach town B, you have to find out how long Richard would take to get there.
3. Two towns, X and Y, were 156 km apart. Tom started to travel from town X to town Y at an average speed of 54km/h. At the same time, Peter also started to travel from town Y to town X. After travelling for 1 and 1/3h, they passed each other on the way. Find the average speed of Peter.
= 72km/ 1 1/3h
= (156 - 72)km/ 1 1/3h
= 84km/ 1 1/3h
Brian: I'm trying to find out the distance Tom has travelled when Tom and Peter met. Then subtract that distance from 156. That would be the distance that Peter had travelled by the time they met, and from this you can find Peter's speed.