Question

A man walks a certain distance with certain speed. If he walks 1/2 km an hour faster, he takes 1 hour less. But, if he walks 1 km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking.

Answer 1

Let the actual speed of the train be x Km/hr and the actual time taken by y hours. Then,

Distance covered= $speed\times time$

If the speed is increased by, then time of journey is reduced by 1 hour i.e., when speed is , time of journey is

Distance covered= km

$xy=(x+\frac{1}{2})(y-1)$

...(ii)

When the speed is reduced by, then the time of journey is increased by i.e., when speed is, time of journey is

Distance covered =

Thus we obtain the following equations

By using elimination method, we have

Putting the value in equation (iii) we get

Putting the value of x and y in equations (i) we get

Distance covered =

=

Hence, the distance is,

The speed of walking is .