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.
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.
[tex]Th\text{e speed of train A =35+x miles per hour.}[/tex]The distance of train A is 340 miles.
Consider the speed formula.
[tex]Speed\text{ =}\frac{distance}{time}[/tex][tex]time\text{ =}\frac{distance}{speed}[/tex]Substitute distance =340 miles and speed = 35+x in the formula to find the time taken by train A to travel 350 miles.
[tex]time\text{ =}\frac{340}{35+x}[/tex]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.
[tex]time\text{ =}\frac{200}{x}[/tex]Train A and B take the same time to travel 350 miles and 200 miles respectively.
Equate both equations of the time.
[tex]\frac{340}{35+x}=\frac{200}{x}[/tex]Use the cross-product method.
[tex]340(x)=200(35+x)[/tex][tex]340x=7000+200x[/tex]Subtract 200x from both sides of the equation.
[tex]340x-200x=7000+200x-200x[/tex][tex]140x=7000[/tex]Divide both sides of the equation by 140.
[tex]\frac{140x}{140}=\frac{7000}{140}[/tex][tex]x=50[/tex]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.
[tex]The\text{ speed of train A = 35+50 miles per hour.}[/tex][tex]The\text{ speed of train A = 85 miles per hour.}[/tex]Final answer:
[tex]T\text{rain A was traveling at 85 miles per hour and train B was traveling at 50 miles per hour}[/tex]