Question

A man walks a certain distance with a 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 man be x km/hr and y be the actual time taken by him in hours. 

So, we know that 

Distance covered = speed x distance

⇒ Distance = x × y = xy …………(i) 

First condition from the question says that, 

If the speed of the man increase by 1/2 km/hr, the journey time will reduce by 1 hour. 

Showing this using variables, we have 

⇒ When speed is (x + 1/2) km/hr, time of journey = y – 1 hours 

Now, 

Distance covered = (x + 1/2) x (y – 1) km 

Since the distance is the same i.e xy we can equate it, [from (i)] xy = (x + 1/2) x (y – 1) 

And we finally get, 

-2x + y – 1 = 0 ………………(ii) 

From the second condition of the question, we have 

If the speed reduces by 1 km/hr then the time of journey increases by 3 hours.

⇒ When speed is (x-1) km/hr, time of journey is (y+3) hours 

Since, the distance covered = xy [from (i)] 

xy = (x-1)(y+3)

⇒ xy = xy – 1y + 3x – 3 

⇒ xy = xy + 3x – 1y – 3 

⇒ 3x – y – 3 = 0 ……………… (iii) 

From (ii) and (iii), the value of x can be calculated by 

(ii) + (iii)

⇒ x – 4 = 0 

x = 4 

Now, y can be obtained by using x = 4 in (ii) 

-2(4) + y – 1 = 0 

⇒ y = 1 + 8 = 9 

Hence, putting the value of x and y in equation (i), we find the distance 

Distance covered = xy 

= 4 × 9 

= 36 km 

Thus, the distance is 36 km and the speed of walking is 4 km/hr.