A cyclist traveling at 26 mph is followed 6 hours later by a car traveling at 78 mph. How long will it take the car to overtake the cyclist?

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