Two trains started from the same place at the same time and

Two trains started from the same place at the same time and traveled in opposite directions at rates that differed by 20 miles per hour. In 5 hours, they were 650 miles apart. Find the rate of each train. Please help!!!

Solution

LET SPEED OF FIRST TRAIN =X MPH
SPEED OF SECOND TRAIN =X+20 MPH
RELATIVE SPEED WHILE TRAVELLING IN OPPOSITE DIRECTIONS =X+X+20=2X+20 =2(X+10)
ORIGINAL DISTANCE OF SEPERATION =0
FINAL DISTANCE OF SEPERATION = 650 MILES
HENCE DISTANCE TRAVELLED =650-0=650 MILES
TIME OF TRAVEL=5 HRS.
SO DISTANCE = RELATIVE SPEED * TIME
650= 2(X+10)*5=10X+100
10X=650-100=550
X=550/10=55 MPH.
SPEED OF FIRST TRAIN =55 MPH
SPEED OF SECOND TRAIN =55+20=75 MPH.