Saturday, April 11, 2009

Speed Problem

I teach maths in Grade 6. There is a word problem in the maths book that I cannot teach using the model method that is usually more suitable for my pupils. The problem: A car and a lorry were travelling towards Town A. The car overtook the lorry when they were 90 km away from Town A. The car arrived at Town A 1/2 h earlier than the lorry while the lorry was 30 km away. Find the average speed of the lorry. Find the average speed of the car.
Please do not think that the model method can be used for all problems. That is not the idea. We want students to learn a variety of heuristics and they should apply it accordingly. Speed problems are rarely solved using the model method. A line diagram is more useful. Please see any Singapore Grade 6 books for such line diagrams.
In the problem posed, the lorry took 1/2 h to finish the last 30 km. So the average speed of the lorry is easily found (60 km/h). With 90 km to go, both the car and the lorry has travelled the same distance from the spot where the lorry started - that was when the car overtook the lorry. The car must be faster but started later.
I want to suspend the solution for a while. I invite readers to continue to solve the problem. Post further question if necessary.

1 comment:

  1. To travel 90km, the lorry takes (90/60) = 1.5 hours.

    Given that the car is 30mins ahead of the lorry, the car takes 1.5-0.5=1 hour to travel the same distance.

    Thus, average speed of the car is 90km/h.

    No use of model was required for solving this question. Rather, deriving the implied information is important. Hope I've helped! (: