Question

A passenger traub keaves a depot 1.5 hours after a freight train leaves the same depot. The passenger train is travleing 18 mph faster than the freight train. Find the rate of each train if the passenger train overtakes the freight train in 2.5h.

Answer 1

Explanation:

At the point where the passenger train overtook the freight train, both trains must have travelled an equal distance.

Let x represent the speed of the freight train.

The passenger train is travelling 18 mph faster than the freight train. This means that the speed of the passenger train would be

x + 18

The passenger train leaves a depot 1.5 hours after a freight train leaves the same depot. if the passenger train overtakes the freight train in 2.5h, it means that total time taken by the passenger train is 2.5h and total time taken by the freight train is 2.5 + 1.5 = 4 hours.

Distance travelled = speed × time

Distance travelled by freight train = 4 × x = 4x

Distance travelled by passenger train = 2.5(x + 18) = 2.5x + 45

Since they travelled equal distances, then

4x = 2.5x + 45

4x - 2.5x = 45

1.5x = 45

x = 45/1.5 = 30

Therefore,

the speed of the freight train is 30 mph and

the speed of the passenger train is x + 18 = 30 + 18 = 48 mph

Answer 2

Speed of passenger train=18+30=48 mph

Speed of freight train=30 mph

Explanation:

Let x be the speed of freight train.

Speed of passenger train=x+18 mph

Time taken by freight train=1.5+2.5=4 hrs

Time taken by passenger train to overtake the freight train=2.5 hrs

Distance=
`Speed* time`

By using this formula

Distance traveled by passenger train=2.5(x+18) miles

Distance traveled freight train=4x

According to question

`2.5(x+18)=4x`

`2.5 x+45=4x`

`45=4x-2.5 x`

`45=1.5 x`

`x=(45)/(1.5)=30`

Speed of freight train=30 mph

Speed of passenger train=18+30=48 mph