Question

A man walks 1 km/hr faster than his usual speed and covers a distance of 3 km in 15 minutes less time. Find his usual speed.

Answer 1

Let the usual speed of man be x km/hr.

Given that when he walks 1 km/h faster than usual, his speed is (x + 1) km/h, and he covers a distance of 3 km in 15 minutes less time than usual.

Using the formula; Time = `"Distance"/"Speed"`

The time it takes for him to cover 3 km at his usual speed × km/h is given by:

Usual time = `3/x​` hr

The time it takes for him to cover 3 km at the faster speed x + 1 km/h is given by:

Faster time = `3/(x+1)`​ hr

The faster time is 15 minutes (`15/60 = 1/4` hours) less than the usual time. Therefore, we can write:

⇒ `3/x - 3/(x+1) = 1/4`

⇒ `(3(x+1) - 3x)/(x(x + 1)) = 1/4`

⇒ `(3x + 3 - 3x)/(x(x + 1)) = 1/4`

⇒`3/(x(x + 1)) = 1/4`

⇒ 3 × 4 = x(x + 1)

⇒ 12 = x² + x

⇒ x² + x − 12 = 0

⇒ x² + 4x − 3x − 12 = 0

⇒ x(x + 4) − 3(x + 4) = 0

⇒ (x + 4)(x − 3) = 0

⇒ (x + 4) = 0 or (x − 3) = 0

⇒ x = −4 or x = 3