Question

Tom took a trip of 1,300 miles. He traveled by train at 50 miles an hour and the same number of hours by plane at 275 mph. How many hours did the trip take? 3 hours 4 hours 8 hours

Answer 1

C. 8 hours.

Explanation:

Let x be the number of hours spent while traveling by train and y represent number of hours spent while traveling by plane.

We have been given that Tom spent same number of hours by plane and by train, so we can represent this information in an equation as:

`x=y...(1)`

The train covers 50 miles in 1 hour, so distance covered by train in x hours would be 50x.

The plane covers 275 miles in 1 hour, so distance covered by plane in y hours would be 50x.

We have been given that Tom took a trip of 1300. We can represent this information in an equation as:

`50x+275y=1300...(2)`

Substituting equation (1) in equation (2) we will get,

`50x+275x=1300`

`325x=1300`

`(325x)/(325)=(1300)/(325)`

`x=4`

Since
`x=y`, therefore,
`y=4`.

To find the total time spent we need to add x and y.

`x+y=4+4=8`

Therefore, the trip took 8 hours and option C is the correct choice.

Answer 2

x/50 = (1300-x)/275

cross multiply

275x = 65000-50x

325x=65000

x = 65000/325 = 200 ( distance traveled by train)

1300-200 = 1100 miles by plane

200/50 = 4 hours by train

1100/275 = 4 hours by plane

4 + 4 = 8 hours