Question

Mohit and Rohit start a simultaneously from two towns P and Q towards Q and P respectively at 8 a.m. R is a check post which is midway between P and Q. Both Mohit and Rohit turn back towards their respective starting points whenever they reach R and every time they reach their starting points they turn back and return to R . If the speeds of Mohit and Rohit are 45km/h and 60km/h respectively and PQ=24km When will they reach R at the same time?

Answer 1

Let distance from point P to R be (X) km then from Q to R = (24 - x) km.

Mohit is from P and his speed is 45km/h.
Distance to R is x km

Time = Distance / Speed

(X / 45) hrs

Rohit travels from Q at a speed of 60km/h.
A distance of (24 - x) km

Time = (24 - x) / 60 hrs

For them to reach R at the same time, the time they take should be equal.

Therefore :

X / 45 = (24 - x) /60

60x = 1080 - 45x

105 x = 1080

x = 72 /7 km

Time = 72/7 × 1/45 = 8/35 hrs

8/35 × 60 = 13 minutes 43 seconds

The time they reach R at the same time is:

8.00 a.m + 13minutes 43 seconds

8 : 13 : 43 a.m.