Question

A freight train leaves a station traveling 60 miles per hour. Thirty minutes later a passenger train leaves the station in the same direction on a parallel track at the speed of 72 miles per hour. How long will it take the passenger train to catch the freight train?

Answer 1

The passenger train will take 2.5 hours to catch the freight train.

Step-by-step explanation

Suppose, it will take
`t` hours for the passenger train to catch the freight train.

As the passenger train leaves the station after 30 minutes or
`(1)/(2)` hour , so the freight train will travel the same distance as the passenger train in
`(t+(1)/(2))` hours.

Speed of the freight train is 60 mph and speed of the passenger train is 72 mph.

As
`Distance = Speed*Time` , so the equation will be......

`72t= 60(t+(1)/(2))\\ \\ 72t= 60t+30\\ \\ 12t=30\\ \\ t= (30)/(12)=2.5`

So, the passenger train will take 2.5 hours to catch the freight train.