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

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What is the answer to our IQ question for October? Did you get it right? Read on to find out more!

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.

One of the possible methods:

1.Runner X and Y ratio is 4:6 (between point A and B, X=4 parts, Y=6 parts)

2.The difference is 2 parts per distance (A to B), therefore to meet each other again,the total distance is twice (2 parts x 2) 3.Hence the difference is 4 parts, which is equal to 160M.

4. If 4parts=160m, then 1 part=40m

5. Since the total is 10 parts, the answer to the distance between A and B = 10 X 40 = 400M

The lucky winner will be announced soon. Stay tuned!

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

1. andrewang Post author

Another possible method:

Since speed X : speed Y = 4 : 6 = 2 : 3, I will divide the total distance into 5 equal parts

X runs 2 units from point A and Y runs 3 units from point B – they will meet at P which is 2 units away from A.

X continues to run 4 units (3 units to B, then back 1 unit) and Y continues to run 6 units (2 units to A, then back 4 units)
– they will meet at Q which is 4 units away from A

Hence PQ = 2 units = 160m,
therefore total distance = 5 units = 400m

2. andrewang Post author

Another possible method using percentage:

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