Two trains, each having a speed of 24 km/h, are headed at each other on the same straight track. A bird that can fly 48 km/h flies off the front of one train when they are 48 km apart and heads directly for the other train ?

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Answer 1 · 2015-09-08T01:36:46

The bird travels 32 km until it meets the other train.

The speed of the train carrying the bird is irrelevant.

Once the bird leaves the train, it can fly at only 48 km/h.

The bird and the train will be travelling for the same time until they meet.

Since #s=vt#, #t = s/v#

Let #1# represent the train and #2# represent the bird.

Since #t_1= t_2#, and

#s_1/v_1=s_2/v_2#,

#s_2/s_1= v_2/v_1 = (48 color(red)(cancel(color(black)("km/h"))))/(24 color(red)(cancel(color(black)("km/h")))) = 2#

(1) #s_1=s_2/2#, and

(2) #s_2 + s_1 = "48 km"#

Substitute Equation (1) into Equation (2):

#s_2 + s_2/2 = "48 km"#

#(3s_2)/2 = "48 km"#

#s_2 = 2/3 × "48 km"#

#s_2 = "32 km"#