SOLUTION: two train start at the same time, one from a to b and other from b to a, if they arrive b and a respectively 3hrs, 12hrs after passed each other. find the ratio between their speed

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Question 761630: two train start at the same time, one from a to b and other from b to a, if they arrive b and a respectively 3hrs, 12hrs after passed each other. find the ratio between their speed?
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Simple diagram given below.
A_______D1_______________________M_____D2______________B

Assume train T1 travels from A to B at speed S1.
Assume train T2 travels from B to A at speed S2.
Let us say they meet at some point M, which is D1 km from A and D2 km from B.
Time taken for T1 to travel from A to M is the same as the time as that taken by T2 to reach M from B.
Since time = Distance / speed,
D1%2FS1+=+D2%2FS2 or D1%2FD2+=+S1%2FS2 (eqn0)
After that, T1 covers distance D2 in 3 hours, while T2 covers distance D1 in 12 hours.
i.e. D1+=+S2+%2A+12 (eqn 1) and D2+=+S1+%2A+3 (e1n 2)
Dividing (eqn 1) by (eqn 2)
D1%2FD2+=+12%2AS2%2F%283%2AS1%29 or D1%2FD2+=+4%2AS2%2FS1 (eqn4)
From (eqn0) and (eqn4)
S1%2FS2+=+4%2AS2%2FS1 i.e. S1%5E2+=+4%2AS2%5E2
Taking positive square roots of both sides

S1+=+2%2AS2 or S1%2FS2+=+2
Ratio of speeds of the two trains is highlight%282%29
:)