A train X starts from station P at 8 am and reaches station Q at 4 pm . Another train Y started from Q at the same time at which X started and reaches P at 3 pm. Then find the time at which both the trains crossed each other .?
Answers
Answer:
11:44 AM
Step-by-step explanation:
Here, we need to understand that distance D is the same for Train X and Train Y.
Let the distance between two points be "D miles”
Speed (S) = Distance (D) / Time (T)
Speed of X = D/8 = D/8 miles/h
Speed of Y = D/7 = D/7 miles/h
Suppose X meets Y after completing traveling ‘x miles’ Traveling for tx hours and Y travelled ty hours.
tx = ty
Time = Speed / Distance
(D/8) / x = (D/7) / (D — x)
=>
x / (D/8) = (D — x) / (D/7)
8x/ D = 7(D — x) / D
=> 8x = 7D — 7x
=> 15x = 7D
=> x = 7D/15
Now, X travels D/8 miles — per hour
To travel 7D/15 miles — How many hours
Number of Hours = (7D/15) x 1 / (D/8)
= 56/15
= 3.733
1 hr — 60 min
0.73 hrs - ? Min = 42 minutes
So, the train X travelled for around 3 hour 42 minutes to meet Y
It started at 8:00 AM. So, it met train Y at 8 + 3 hr 42 minutes = 11:42 A.M ≈ 11:44