Peter and Rhea live some distance apart from each other, separated by a straight road. They both take out their cars and start driving at the same time at the same speed toward each other's home.

After some time, their cars meet 500 miles away from Peter's house. They keep driving and reach at each other's home. Without stopping by, they turn back and start driving again. This time, they meet 300 miles away from each other's home.

What is the distance between their houses?

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IreneIQviz IreneIQviz · Answer 1

Let the distance between Peter's (hereafter referred as P) and Rhea's (hereafter referred as R) be D.

When P and R meet for the first time, P has traveled 500 miles.

In that case, R has traveled (D - 500) miles.

=> Speed of P / Speed of R = 500 / (D - 500) (1)

When P and R meet for the second time, P has traveled (D - 500) + 300 miles

Now, R has traveled (500 + D - 300)

=> Speed of P / Speed of R = 5 / (D - 5) (2)

Equating (1) and (2)

500 / (D - 500) = (D - 2) / (D + 2)

D = 1200 Miles.