Question

Aand B are two stations 600 km. apart. Two trains start simultaneously fromA and B, each to the opposite stations. The train from A reaches B ninehours, the train from B reaches Afour hours after they meet. Find the rateat which each train travels.​

Answer 1

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A_______________________B

60 km

Speed of train A = distance/time

= 600/9

= 200/3 km/h (or 66.67km/h)

Let the speed of train B

= x km/h

Relative speed

= 200/3 + x

Time taken to meet

= 600/(200/3 + x)

B reaches A, four hours after they meet

∴ Time taken by B to reach A

= 600/(200/3 + x) + 4

But time taken by B to reach A

= distance/speed

= 600/x

So,

600/(200/3 + x) + 4 = 600/x

This simplifies to

3x^2 + 200x - 30000=0

Solve this using quadratic formula:

x = [-b+/-√b^2-4ac]/2a

a=3, b=200, c= -30000

x = 72.08

Speed of A = 66.667km/h

Speed of B = 72.08km/h

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