Question

Train A has a speed 35 miles per hour greater than that of train B. If train A travels 340 miles in the same times train B travels 200 miles, what are the speeds of the two trains?Train A was traveling atmiles an hour where train B was traveling at_ miles per hour where train B was traveling at _ miles per hour. I

Answer 1

Given:

Train A has a speed of 35 miles per hour greater than that of train B.

If train A travels 340 miles at the same time train B travels 200 miles.

Required:

We need to find the speed of each train.

Step-by-step explanation:

Let x miles per hour be the speed of train B.

The speed of train A is 35 miles per hour greater than x miles per hour.

`Th\text{e speed of train A =35+x miles per hour.}`

The distance of train A is 340 miles.

Consider the speed formula.

`Speed\text{ =}(distance)/(time)`
`time\text{ =}(distance)/(speed)`

Substitute distance =340 miles and speed = 35+x in the formula to find the time taken by train A to travel 350 miles.

`time\text{ =}(340)/(35+x)`

The distance of train B is 200 miles.

Substitute distance = 200 miles and speed =x in the formula to find the time taken by train B to travel 200 miles.

`time\text{ =}(200)/(x)`

Train A and B take the same time to travel 350 miles and 200 miles respectively.

Equate both equations of the time.

`(340)/(35+x)=(200)/(x)`

Use the cross-product method.

`340(x)=200(35+x)`
`340x=7000+200x`

Subtract 200x from both sides of the equation.

`340x-200x=7000+200x-200x`
`140x=7000`

Divide both sides of the equation by 140.

`(140x)/(140)=(7000)/(140)`
`x=50`

We get that the speed of train B is 50 miles per hour.

Substitute x =50 in the speed of train A =35+x miles per hour.

`The\text{ speed of train A = 35+50 miles per hour.}`
`The\text{ speed of train A = 85 miles per hour.}`

Final answer:

`T\text{rain A was traveling at 85 miles per hour and train B was traveling at 50 miles per hour}`