## Monday, April 13, 2009

### Another Speed Problem

I have a word problem about speed that I cannot explain to my pupils easily.

Car A and Car B left Town X for Town Y at the same time. Car A was travelling at an average speed of 80 km/h and Car B was travelling at an average speed of 60 km/h. Car A was leading Car B by 8 km for every 1/6 of the distance from Town X to Town Y. Find the distance between Town X and Town Y. One of my friends solve it like this: 6 units x 8 km = 48 km and 80 km - 60 km = 20 km. 80 : 20 = 4. Hence, the distance from Town X to Town Y = 4 x 48 = 192 km. However, the solution is too difficult for my pupils.
Charmaine's Suggestion:

Car A travels 20km more than Car B in an hour. (80-60)
Since Car A leads Car B by 8km for 1/6 of the journey, it leads by a total of 8*6 =48km for the entire journey (6/6).
Thus, time taken for the whole journey by A: 48/20hours = 12/5 hours (leave in simplest improper for easier calculation later...)
Distance between X and Y is thus 12/5*80 = 192km.
Seow's Suggestion

1. Car A travels 20km more than Car B in an hour. (80-60)

Since Car A leads Car B by 8km for 1/6 of the journey, it leads by a total of 8*6 =48km for the entire journey (6/6).

Thus, time taken for the whole journey by A: 48/20hours = 12/5 hours (leave in simplest improper for easier calculation later...)

Distance between X and Y is thus 12/5*80 = 192km.

Hope that helps! (:

2. Hi,
Hope this helps.
http://farm4.static.flickr.com/3648/3457754184_35d7fcdc47_o.jpg