Question

A man cover a certain distance by 10 km/hr and becomes 15 minute late. But if he travel the same distance with 12 km/hr then he becomes 5 min late find the distance?

Answer 1

Let the distance = x km

Case 1 :- man covers a certain x km distance by 10 km/h and becomes 15 minutes late .
Let original time taken by man = T hr
∵ time = distance/speed
∴ ( T + 15/60 ) = x/10 [ ∵ 15 minutes = 15/60 hr]
⇒T + 1/4 = x/10 ------(1)

Case 2 :- man when travel same distance by 12 km/h , he becomes 5 min late .
∴ (T + 5/60 ) = x/12 [ ∵ 5 minutes = 5/60 hr ]
⇒T + 1/12 = x/12 ------(2)

Subtracting equation (2) from (1),
(T + 1/4) - (T + 1/12) = x/10 - x/12
⇒1/4 - 1/12 = 2x/120
⇒(3 - 1)/12 = x/60
⇒1/6 = x/60
⇒ x = 10

Hence, distance = 10 km

Answer 2

Solution :-

Let the distance be 'x' km

We know that, Time = Distance/Speed

Time taken by the man if he rides at 10 km/hr = x/10 hr

Time taken by the man if he rides at 12 km/hr = x/12 hr

Difference of time = 15 minutes - 5 minutes

= 10 minutes = 1/6 hr

x/10 - x/12 = 1/6

Taking LCM of the denominators and then solving it.

⇒ 6x - 5x = 10

⇒ x = 10

So, the distance is 10 km.

Answer.