A cyclist traveling at 26 mph is followed 6 hours later by a car traveling at 78 mph.
Let x be the time taken by the cyclist
Speed of the cyclist = 26 mph
WE know distance = speed * time
so distance traveled by cyclist = 26*x
car started 6 hours later
(x-6) is the time taken by the car
Speed of the car = 78 mph
distance traveled by car = 78(x-6)
when the car overtakes the cyclist then the distance becomes same
so 26x= 78(x-6)
solve for x
26 x = 78x - 468
Subtract 78x on both sides
-52x = -468
Divide both sides b y 52
so x= 9
Time taken by the cyclist = 9 hours
car started 6 hours later
So time taken by the car = 9-6 = 3 hours
it will take 3 hours for the car to overtake the cyclist
