Question

A Metra commuter train leaves Union Station in Chicago at 12 noon. Two hours later, an Amtrak train leaves on the same track, traveling at an average speed that is 50 miles per hour faster than the Metra train. At 3 PM the Amtrak train is 10 miles behind the commuter train. How fast is each going?

Answer 1

Metra train is going at 30 mph.

Amtrak train is going at 80 mph.

Explanation:

Let s be the speed of the Metra commuter train.

Then the speed of Amtrak train will be =
`s+50`

Distance traveled by the commuter train at 3pm = 3s

Distance traveled by Amtrak train at 3 pm =
`1(s+50)`

We know that distance = speed x time

commuter distance = Amtrak distance + 10 miles

`3s= 1(s+50)+10`

`=> 3s=s+50+10`

`=> 3s=s+60`

`=> 3s-s=60`

`=> 2s=60`

So, s = 30 mph

The Metra commuter is going at 30 mph.

The Amtrak train is going at
`30+50=80` mph