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 ?

1 Answer
Sep 8, 2015

Answer:

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

Explanation:

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"#