Question

The distance between two cities A and B is 330 km. A train starts from A at 8 am and travels towards B at 60 km/hr. Another train starts from B at 9 am and travels towards A at 75 km/hr. At what time they meet.
a. 1:00 pm
b. 11:00 am
c. 4:00 pm
d. 12:00 noon

Answer 1

Hint: We first assume x in terms of time trains meeting and form an equation according to question, then solve for x. Add x hours to starting time.

Complete step-by-step answer:
Assume that they meet x hours after 8 am then, train 1, starting from A travel x hour till the train meet
Distance travelled by train 1 in x hour = 60x km.
Train 2, starting from B, travels (x – 1) hours till the train meets.
Distance travelled by train 2 in (x – 1) hours. Total distance travelled = Distance travelled by train 1 + Distance travelled by train 2.
⇒ 330 = 60x + 75(x – 1)
⇒ 12x + 15(x – 1) = 66
⇒ 12x + 15x – 15 = 66
⇒ 27x = 66 + 15 = 81
⇒ 3x = 9
⇒ x = 3.
Hence the train meets 3 hour after 8 am i.e. 11 am
So, from the above option B option is only correct.

Note: We can solve by this method also. Train 1 starting from A, travels 60 km in first hour, Hence at 9 am both train are 330 – 60 = 270
Apart and relative speed is 60 + 75 = 135 kmph
Time needed now for the trains to meet $ = \dfrac{{270}}{{135}} = 2h$
i.e. the trains meet 2 hour after 9 am
i.e. 11 am.