Question

A passenger train leaves the Detroit and travels toKansas Cityat a speed of 135 km/h. A diesel train leavesDetroit at the same time traveling in the opposite directionwith an average speed of 112 km/h. How many hours mustthe diesel train travel until it's exactly 741 km away fromthe passenger train?

Answer 1

Data:

Passenger train: P

speed: 135 km/h

Diesel train: D

speed: 112 km/h

The distance is equal to the speed multiplied by the time. You have the next equation that represent the distance travel by each train in terms of time (x) (in hours)

`\begin{gathered} P=135x \\ D=112x \end{gathered}`

As the trains go in opposite direction and leave Detroit at the same time. They are 741 km away when the sum of their distances travel is 741km:

`\begin{gathered} P+D=741 \\ \\ 135x+112x=741 \end{gathered}`

Solve x in the equation above to find the time that takes the trains to be 741 km away:

`\begin{gathered} 247x=741 \\ x=(741)/(247) \\ \\ x=3 \end{gathered}`

Answer: After 3 hours of travel the diesel train is 741km away from the passenger train