Question

Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 40 miles per hour. How far from the station was train A overtaken by train B?

(A) 180
(B) 240
(C) 270
(D) 300
(E) 320

Answer 1

(B) 240 miles

Step-by-step explanation:

As the two trains move uniform motion we apply the following equation:

d= v*t

Where:

d= displacement in miles ( mi)

v= speed in miles per hour (mph).

t= time in hours (h)

Data

vA = 30 mph

vB = 40 mph

tA = ( tB+2 ) h

Kinematic equation of train A

dA= vA*tA

dA= 30*tA Equation (1)

Kinematic equation of train A

dB= vB*tB

dB= 40*tB Equation (2)

Problem development

When train A is overtaken by train B, then, dA = dB

Equation (1) = Equation (2)

30*tA = 40*tB , tA=tB+2

30*(tB+2 )= 40*tB

30*tB + 60 = 40*tB

60 = 40*tB - 30*tB

60 =10*tB

tB =60/10

tB =6 h

We replace tB =6 h in the equation (2)

dB= 40*6

dB= 240 miles