Pei Chun Public Sch 2007 PSLE Math Prelim Q47

Najip, Kumar and Gurmit started jogging at the same time from the same starting-point round a circular track. Najip and Kumar jogged in a clockwise direction and Gurmit jogged in an anti-clockwise direction. Gurmit took 5 minutes to complete each round. Gurmit met Najip after every 3 minutes. Gurmit met Kumar after every 2 minutes. The jogging speed of each person remained the same throughout.
a) What was the ratio of Gurmit’s speed to Najip’s speed to Kumar’s speed?

b) When Gurmit and Najip met again at the starting-point after 15 minutes, Kumar had already jogged 3.6 km. What is the circumference of the circular track?



b)
(Gurmit)
5 min ----- 1 round
15 min ----- 3 rounds

Kumar (since ratio Gurmit : Kumar is 2:3) ----- 4.5 rounds
3.6 km divided by 4.5 rounds = 0.8 km per round

Answer: The circumference is 0.8 km

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Update - 1420 hours, 29 Aug 2008

I have relabelled the model to make it clearer.
The model is seen from Gurmit’s perspective.
He was running in the opposite direction as compared to the other two.

In the 5 min cycle, Gurmit will see Kumar after 2 min.
This means G would have covered 2/5 of lap when he met K.
It also means K would have covered 3/5 lap at that point.
Hence, the model shows 2 units for G and 3 for K.

In the same 5 min cycle, G will meet N after 3 min.
This means G would have covered 3/5 lap when he met N.
Of course, N would have covered 2/5 lap.
Hence, 3 units for G and 2 for N.