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Coming back from Boston by train a passenger missed his station and got off the train at a station beyond which there remained 13/24 of the train’s total route. The passenger needs to go 14 miles to get back to his own station. If the distance from Boston to the passenger’s station is one third of the train’s total route, how long is this route?

The total distance of the route is 112miles.

Step-by-step explanation:

Let us consider the total distance of the route to be 'y'.

Given that,

The distance from Boston to the passengers station = (1/3) y

The passenger got down at a station after beyond his station which is 14 miles away and the remaining route from that station is (13/24) y

So the travelled route = y - (13/24) y

= (11/24) y

The travelled route is from Boston to a station beyond 14miles of his station.

We can write the above as,

(11/24) y = (1/3) y + 14

(11/24) y - (1/3) y =14

(11y - 8y) /24 = 14

3y/24 = 14

y/8 = 14

y = 14 x 8

y = 112 miles

The total distance of the route is 112 miles

112

Step-by-step explanation:

14 miles makes up 11/24 - 1/3 = 1/8 of the total route. The total route is 8*(14 miles) = 112 miles.

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