Coming back from boston by train a passenger missed his station and got off the train at a station beyond which remained 13/24 of the whole train route. The passenger needs to go 14 miles to get back to his own station. If the distance from boston to the passengers station is a third of the trains total route. How long is this route

This route is 112 miles long.

Step-by-step explanation:

Let's say that the passeneger meant to get off at Station A but instead got off at Station B. We are told that the distance from Boston to Station A is 1/3 of the train's total route. Let's say that the train's total route is x miles long. Now we can say that the distance from Boston to Station A is 1/3x.

We are told that the distance from Station A to Station B is 14 miles.

We are also told that the distance from Station B to the end of the route is 13/24 of the whole route. Since we already decided that the whole route is x miles long, we can say that the distance from Station B to the end route is 13/24x.

Add up all of these distances to get the total distance of the trains route:

13/24x+14+1/3x=x.

14+13/24x+8/24x=x

14+21/24x=x

14=3/24x

14=1/8x

112=x

Hope this helps!

112

Step-by-step explanation: