A leaves station P at 8:00 a.m. and reaches station Q at 11:00 a.m. B leaves station Q at 9:00 a.m. and reaches station P at 11:00 a.m. At what time will they cross each other?

9:48 a.m.

Time taken by the first train = 3 hours

Time taken by the second train = 2 hours

Ratio of time taken by the two trains = 3 : 2

As we know, the ratio of speed will be the opposite of the ratio of time taken .

So ratio  of speed = 2 : 3

Let the distance travelled by the two trains = 2 × 3 = 6 km

DIstance = (Speed × time)

Before the second train started, the first train already travelled for 1 hour

Thus, the distance travelled by the first train in 1 hour = 2 × 1 = 2 km

Distance remaining = 6 - 2 = 4 km

Thus, the time of meeting =   \(\frac{4}{3 + 2 }\)

Relative speed = 3 + 2 = 5 ( when moves towards each other )

= \(\frac{4}{5}\)

= 48 minutes

So , They meet at 9:00 am + 48 minutes = 9:48 am