Answer to Question #90801 in Algebra for Shifa naaz

Question

A man, stride is cm long and his wife stride is 15 cm shorter. He covers 30m in 10 steps less than his wife. frame an equation in x and solve it

Answer 1

Let the man's stride be x cm.

Then the wife's stride is (x - 15) cm.

The distance that they cover is 30 m = 3000 cm.

The number of steps taken by man in 30 m is 3000/x.

The number of steps taken by wife in 30 m is 3000/(x - 15).

As the man covers 30 m in 10 steps less than his wife, we get the equation:

3000/(x - 15) - 10 = 3000/x

3000x - 10x(x-15) = 3000(x -15)

3000(x - x + 15) - 10(x2 - 15x) = 0

3000 * 15 = 10(x2 - 15x)

x2 - 15x - 4500= 0

x2 - 75x + 60x - 4500 = 0

x(x - 75) + 60(x - 75) = 0

(x - 75)(x + 60) = 0

x = 75 cm

x - 15 = 60 cm

Thus, the man's stride is 75 cm and the wife's stride is 60 cm.