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A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr . the other one walks at 5.4 km/hr.
The train needs 8.4 and 8.5 seconds respectively to overtake them.
What is the speed of the train if both the persons are walking in the same direction as the train?
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Let "u" be the train speed (in 
), now unknown, and
let L be the train length, in meters.
8.4 sec. = 
minute, 8.5 sec. = 
minute.
4.5 
= 75 
, 5.4 = 90 .
Two equations for two unknowns:
= L, (1)
= L. (2)
Since the right sides of (1) and (2) are equal, then their left sides are equal too:
= , (3)
and we excluded one unknown L.
Multiply both sides of (3) by 60. You will get
8.4*u - 75*8.4 = 8.5*u - 90*8.5,
90*8.5 - 75*8.4 = 8.5u - 8.4u,
0.1u = 135 ---> u = 
= 1350 = 81 .
Answer. The speed of the train is 81 .
