SOLUTION: A car left the town at a constant speed of 60 kph. 2 hours later, a policeman on a motorcycle at a constant speed of 80 kph also left the town and pursued the car. How long did it
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-> SOLUTION: A car left the town at a constant speed of 60 kph. 2 hours later, a policeman on a motorcycle at a constant speed of 80 kph also left the town and pursued the car. How long did it
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Question 1117112: A car left the town at a constant speed of 60 kph. 2 hours later, a policeman on a motorcycle at a constant speed of 80 kph also left the town and pursued the car. How long did it take the motorcycle to overtake the car? How far did the motorcycle travel? Answer by greenestamps(13200) (Show Source):
In the 2 hours that the car traveled before the policeman started, the car traveled 60*2 = 120 km. So when he starts, the policeman has to make up 120 km to overtake the car.
The policeman travels at a rate 80-60 = 20 kph faster than the car.
The number of hours the policeman has to travel, making up 120 km at a rate of 20 kph, is 120/20 = 6.
So the policeman traveled for 6 hours before overtaking the car; in 6 hours at 80 kph he traveled 80*6 = 480 km.
Algebraically....
Let x be the number of hours the policeman traveled
Then x+2 is the number of hours the car traveled
We want to know when the distances traveled are the same -- the car for x+2 hours at 60 kph and the motorcycle for x hours at 80 kph:
