Question

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?

Answer 1

Answer:

36 hours

Step-by-step explanation:

let,

1st train speed = v1 km/h, and

2nd train speed = v2 km/h

use,

${ \frac{v1}{v2} } = \sqrt{ \frac{t2}{t1} } = \sqrt{ \frac{25}{16} } = \frac{5}{4} \\ v2 = \frac{4v1}{5}$

A/Q,

3 hours after they met, they were 675 Km apart

so,

3v1+3v2 = 675

v1 + v2 = 225

v1 + 4v1/5 = 225

9v1/5 = 225

v1 = 225x5/9 = 125 km/h, then

v2 = 4v1/5 = 4x125/5 = 100 km/h

Now,

P-------|-------------Q

16h 25h

PQ = 16v1+25v2 = 16x125+25x100 = 4500km

so,

Time taken by the first train to complete the journey = PQ/v1 = 4500km/125km/h = 36h.