# CAT Practice : Speed Time, Races

## Trains A and B

Q.28: Two trains left from two stations P and Q towards station Q and station P respectively. 3 hours after they met, they were 675 Km apart. First train arrived at its destination 16 hours after their meeting and the second train arrived at its destination 25 hours after their meeting. How long did it take the first train to make the whole trip?
1. 18h
2. 36h
3. 25h
4. 48h

Choice B.36h

## Detailed Solution

Total distance travelled by both the trains before meeting = D. This distance will be covered in the proportion of their speeds. Clarify with the diagram.

3 hours after meeting distance travelled by A = SA x 3 and by B = SB x 3

Therefore, 3 (SA + SB) = 675 =) SA + SB = 225.

Now the remaining distance to be covered by first train is DSB/(SA + SB). Therefore, time taken = $\frac{DS_B}{(S_A + S_B)S_A} = 16$ ---------- (1)

Similarly, $\frac{DS_A}{(S_A + S_B)S_B} = 25$ ---------- (2)

Dividing equation 1 by 2 -

$\frac {S_A^2}{S_B^2} = \frac{25}{16} => \frac{S_A}{S_B} = \frac{5}{4}$. Therefore, $S_A + \frac{4}{5} * S_A = 225$ => SA = 125 Km/hr and SA = 100 Km/hr

From equation 2, $\frac{D}{S_A} = 16 * \frac{(S_A + S_B)}{S_B} = 16 * \frac{225}{100} = 36$ h which is the time taken for the first train to complete the journey.

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## More questions from Speed Time, Races

"Life is a race ... if you don't run fast ... you will be like a broken undaa" - Veerusahasra Buddhi