Question

Suppose two trains leave a certain​ station, at the same​ time, traveling in opposite directions. one train travels 1010 mph faster than the other. in 2.52.5 ​hours, the trains are 255255 miles apart. find the speed of each train.

Answer 1

In the question, it is given that

Suppose two trains leave a certain​ station, at the same​ time, traveling in opposite directions. one train travels 10 mph faster than the other. in 2.5hours, the trains are 255 miles apart.

Let the speed of the slower train be x m/h and faster train be (x+10) m /h.

Distances travelled by them are

$d_{slower} = 2.5 x \ miles, d_{faster} = 2.5(x+10) miles$

And total distance is 255 miles, that is

$2.5x +2.5(x+10) = 255 \\ x+x+10=102 \\ 2x = 92 \\ x = 46 MPH$

So the speed of slower train is 46 MPH and of faster train is 56MPH.