Find the speed of each train.

Question

The speed of a passenger train is 12 mph faster than the speed of a freight train. The passenger train travels 280

miles in the same time it takes the freight train to travel 220 miles. Find the speed of each train.

The speed of the passenger train is _______ mph.

The speed of the freight train is ________ mph.

Answer 1

We will take formula D = RT

As the passenger train is 12mph faster than freight train, so for passenger train

D =RT

280 = (R +12)T

T = 280 / R + 12

For Freight train

220 = RT

T = 220/ R

As time taken by both trains is same, so

280 / R + 12 = 220/ R (we will cross multiply)

280 R =220R + 2640

280 R - 220R = 2640

60 R = 2640

R = 2640/60

R = 44mph (for freight train)

As the passenger train is 12mph faster than freight train, so value of R for passenger train will be 44 + 12 = 56mph.

you can also check your answer by putting these values in formula T = D/R as time is same for both trains

T(P) = T(F)

D/R = D/R

280/56 = 220/44

5 = 5

Answer 2

d = rt

t = d/r

The times are the same.

280/(r + 12) = 280/r

Cross multiply!

280r = 220(r + 12)

280r = 220r + 2640

60r = 2640

r = 44

44 + 12 = 56

The speed of the passenger train is 56 mph.

The speed of the freight train is 44 mph.