# IQ Test (October): Was it complicated, or did you complicate it?

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Here is another IQ test for everyone. Again, this is a primary 6 Mathematics question. If it takes you more than “4 steps” to do it, then you have just complicate matters unnecessarily. I was “stunned’ by this question for  more than an hour just to find a simple solution.  Try it, give it a shot and post your answer in the comment box. ALL ARE WELCOME!

DIFFICULTY Level: 3 out of 5 Stars

QUESTION:

Runner X and Runner Y jogged to and fro repeatedly along a straight path between point A and B. Runner X jogged at a uniform speed of 4 M/s and Runner Y jogged at a uniform speed of 6 M/s. They started jogging from opposite direction at the same time as shown:

They first met one another at point P. The second time they met each other was at point Q. Given the distance between P and Q is 160M, Find the distance between A and B.

## 16 thoughts on “IQ Test (October): Was it complicated, or did you complicate it?”

1. Ngo Chon Thao

6AP = 4PB = 4S – 4AP
=> AP = 2/5S (1)

6S + 6QB = 4S + 4AQ = 4S + 4S – 4QB
=> QB = 1/5S (2)

S = AP + 160 + QB = 2/5S + 160 + 1/5S
=> S = (160 x 5)/2 = 400m

2. andrewang Post author

For those that have attempted and couldn’t get the answer, it is ok. The courage to attempt,is itself, the first step of a journey. Leave your ‘footprint’ behind by dropping a comment that you have attempted it. Then, come back and fight another day!

3. JA

Spot this on blog browsing, kinda given a shot with primary 6 explanation:-

Given X’s speed = 4 m/s
Y’s speed = 6 m/s

and knowing Time = Distance/ Speed

At point P where X&Y meet, they spent same time of travel therefore:-

AP / 4 = BP / 6
AP = 4/6 BP (EQ 1)

Same goes to point Q they meet each other:-

(AP + BP + BP – 160)/4 = (AP + BP + AP +160)/6
AP = 4BP – 800 (EQ 2)

Solving EQ 1&2 get, AP = 160 and BP = 240

Total distance = AP + BP = 400m

Full mark???

4. Mark Ong

Hi everyone, thank you for your participation. There is still more time before this contest is concluded, therefore, keep those answers coming!

5. sklooi

If A to B is 0 to 100% and given the speed of runner x is 4m/s and runner y is 6m/s.
So the 1st meet point P is 40% of the distance of A to B.
with this same speed, the 2nd meeting point Q will be on the 3rd set of the run, where Runner x will reach B(100%) and back and runner y to A(0%) and back and it is 80% of the distance of A to B.
Given distsnce of P and Q (80% -40% = 40%) is 160m. so 100% is 400m