This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

Friday, August 29, 2008

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.

8 comments:

keentolearn said...

Dear Mr Song

Wish to seek your clarification .

Kumar’s speed is faster than that of Gurmit, why is 2min to 3 min for G:K in the model.Also why is 3min:2min for G:N as Gurmit is faster.

Best Wishes

Excel Eduservice said...

I have relabelled the model to make it clearer. Thanks for the highlight.

Excel Eduservice said...

I have relabelled the model to make it clearer. Thanks for the highlight.

keentolearn said...

Dear Mr Song,

Thank you for your super fast reply. Please help to see if you have any similar type of question in your databases.

Sarah took 15 minutes to jog from her home to a swimming pool. After swimming, she took 20 minutes to walk the same way home. Her walking speed was 3 km/h slower than his jogging speed. Find Sarah's walking speed in km/h.

keentolearn said...

Dear Mr and Mrs Song

Wishing you a very Happy Teacher's Day.

Best Wishes

keentolearn said...

Dear Mr and Mrs Song

Wishing you a very Happy Teacher's Day.

Best Wishes

Excel Eduservice said...

Keentolearn: Wishing you a very Happy Teacher's Day.

Me: Thanks.

Jog ----- 15 min
Walk ----- 20 min

Time
Jog : Walk
3 : 4

Distance covered (jog will cover more dist because of greater speed)
Jog : Walk
4 : 3

1 unit difference ----- 3 km/h
(Walk) 3 units ----- 9 km/h (Ans)

Observer said...

It sounds a bit confusing to say that the distance covered is more for jogging than walking when the distances covered in both jogging and walking are the same.

It might be clearer to use the Speed formula D = S x T

D = SJ x 15 = SW x 20
SJ = (4/3) SW

SJ - SW = 3

So (1/3) SW = 3
SW = 9 km/h