two cars started at the same time from towns 50 km apart and

two cars started at the same time from towns 50 km apart and travelled toward each
other at uniform speed. They meet in 20 minutes and immediately started off again,
but this time, in the same direction, travelling at the same rates as before. Soon after,
the slower car stopped for 30 minutes and then started as usual. At what rate did each
car travel if, two hours after they started for the third town, they were 55 km apart?

Solution

LET THE SPEED OF FASTER CAR =F KMPH
AND SPEED OF SLOWEWR CAR =S KMPH
I LEG
DISTANCE OF SEPERATION AT START= 50 KM
RELATIVE VELOCITY=F+S
TIME REQUIRED TO MEET =50/(F+S) HRS=20/60=1/3 HR
F+S=150............I
II LEG
DISTANCE OF SEPERATION AT START =0
TIME OF TRAVEL FOR SLOWER CAR = 2-30/60=2-0.5=1.5 HRS
DISTANCE TRAVELLED BY SLOWEWR CAR =1.5S KM
TIME OF TRAVEL FOR FASTER CAR = 2 HRS
DISTANCE OF TRAVEL BY FASTER CAR =2F KM
DISTANCE OF SEPERATION AT THE END =2F-1.5S=55...................II
EQN.I*2-EQN.II
2F+2S-2F+1.5S=2*150-55=300-55=245
3.5S=245
S=245/3.5=70 KMPH
F=150-70=80 KMPH