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.

Gita

*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.*

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

ReplyDeleteGiven 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! (: