Question

A father and a son are playing a game of catch.after he runs 27 steps,his father starts running.after he runs 27 steps,his father starts running behind him.the father runs faster.for every 8 steps the son takes,father takes 5 steps.in addition,2 steps of the father are equal in length to the son's 5.how many steps did the father have to take to catch the son?

Answer 1

Let father have to take x steps to catch the son.

A/C to question,
2 steps of the father = 5 steps of the son
means 5 steps of the father = 12.5 steps of the son .

now , for every 8 steps takes the son , father takes 5 steps .
means every 8 steps of son, father take 12.5 steps { comparison with the steps of son }
it means every 8 steps of son , father close to son by (12.5 - 8) = 4.5 steps .

so, now, Let y times they have to require to approach each other ,
then, 27 - 4.5y = 0 { because every 8 steps of son close with him by 4.5 steps }
27 = 4.5y => y = 6

hence, number of steps have to take by father to catch the son = total times of 5 steps taking by father × 5 steps = 6 × 5 = 30 steps

answer = 30 steps

Answer 2

your answer is 30 steps