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

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?”

Chan Chek Jin October 14, 2010 at 7:22 pm

Answer: 400m

-Editor’s note: Working has been omitted out.-

Siang Leng October 14, 2010 at 9:10 pm

Answer: 160m+160m+80m = 400m or 0.4km

Chris liu October 15, 2010 at 12:27 am

800

Francis Nio October 15, 2010 at 8:31 am

400m

Ngo Chon Thao October 16, 2010 at 2:37 pm

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

andrewang Post authorOctober 17, 2010 at 11:09 am

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!

SY October 18, 2010 at 10:30 am

400

JA October 19, 2010 at 11:27 pm

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???

Mark Ong October 20, 2010 at 9:06 am

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

Jov October 21, 2010 at 1:44 am

Ans is 560m

sklooi October 21, 2010 at 5:51 pm

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