two trains start simultaneously from two tunnels towards each other. the first train covers 8% of the distance between the two tunnels in 3 hours the second train covered 7/120 of the distance in 2 hours 30 minutes. find the speed (feet/h) of the second train. if the first train travelled 800 feet to the meeting point:
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Let the total distance be x.
First train
Distance = 0.08x
Time = 3 hrs
Speed = 0.08x/3
The distance covered to reach meeting point is = 800 feet
The time = 800/(0.08x/3) = 2400/0.08x
The second train
The distance covered = 7/120 x
Time taken = 2.5 hrs
The speed = 7/120x × 1/2.5 = 7/300x
The distance covered to reach meeting point is = x - 800
The time = (x - 800) / (7/300x)
300(x - 800) /7x = (300x - 240000) / 7x
The two trains take equal time to reach the meeting point hence we equate the two times as follows.
2400/(0.08x) = (300x - 240000) / 7x
7x(2400) = 0.08x(300x - 240000)
16800x = 24x² - 19200x
16800x + 19200x = 24x²
36000x = 24x²
Dividing through by 24x² we have :
x = 36000/24
x = 1500 feet.
Speed of the second train is :
7/300 × 1500 = 35 feet per hour
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