Question

A cargo grain leaves Chicago at noon travelling west at 120 km/h. At 2 pm, a passenger train leaves Chicago travelling east at 360km/h. What time will it be when the trains are 1520 km apart? At that time, what distance has each train travelled?

Answer 1

a) The trains will be 1520 km apart at 2:40 pm for the cargo train and at 4:40 pm for the passenger train.

b) At that time the cargo train has traveled 560.04 km and the passenger train has traveled 960.12 km.

Explanation:

a) First, we need to find the distance traveled by the cargo train in the two hours before the passenger train leaves Chicago:

`x_(1) = v_(1)t_(1) = 120 km/h*2h = 240 km`

Now, we can find the time when the trains will be 1520 km apart:

`1520 km = (x_(1) + 240 km) + x_(2)`

Where 1 is for the cargo train and 2 is for the passenger train.

`1520 km = (v_(1)*t_(1) + 240 km) + v_(2)t_(2)`

Since we need to calculate the time when the trains are 1520 km apart, t₁ = t₂, so:

`1520 km = (v_(1)*t + 240 km) + v_(2)t`

`t = (1520 km - 240 km)/(120 km/h + 360 km/h) = 2.667h`

For the cargo train, it will be 1520 km apart from the passenger train at:

`t_(1) = 12 pm + 2 h + 40 min = 2:40 pm`

And for a passenger train, it will be 1520 km apart from the cargo train at:

`t_(2) = 2 pm + 2 h + 40 min = 4:40 pm`

Hence, the trains will be 1520 km apart at 2:40 pm for the cargo train and at 4:40 pm for the passenger train.

b) The distance traveled by both trains is given by:

`x_(1) = v_(1)*t + 240 km = 120 km/h*2.667 h + 240 km = 560.04 km`

`x_(2) = v_(2)*t = 360 km/h*2.667 h = 960.12 km`

Therefore, at that time the cargo train has traveled 560.04 km and the passenger train has traveled 960.12 km.

I hope it helps you!