two cyclists starts from the same point and ride in opposite

two cyclists starts from the same point and ride in opposite directions. onecyclist rides 5 mph faster than the other. in 5 hour the cyclists are 175 miles aparT. find the rate of the slower cyclist.

Solution

Let x = speed of slower cyclist, A
therefore x+5 = speed of faster cyclist, B.

Both A and B travel for 5 hours
Let A travel distance d, so B must travel distance 175-d.

Right, speed = distance/time, so

A: x = d/5
--> d = 5x

B: x+5 = (175-d)/5
--> 5(x+5) = 175-d
--> 5x+25 = 175-d
--> d = 175 - (5x+25)
--> d = 175 - 5x - 25
--> d = 150 - 5x.

So, equate both these for d to get rid of d, since that is something we are not interested in, so 5x = 150 - 5x

10x = 150
x = 15mph --> speed of A
hence B travels at 20mph