SOLUTION: A car traveling at 45 mph overtakes a cyclist who, riding at 20 mph, had a 2-hour head start. How far from the starting point does the car overtake the cyclist?

Question 1187050: A car traveling at 45 mph overtakes a cyclist who, riding at 20 mph, had a 2-hour head start. How far from the starting point does the car overtake the cyclist?

Found 3 solutions by ikleyn, greenestamps, MathTherapy:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
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Let t be the travel time of the car (in hours); then the travel time of the cyclist is (t+2) hours. The distance equation is 45*t = 20*(t+2). Simplify and find t 45t = 20t + 40 45t - 20t = 40 25t = 40 t = = hours = 1 hours = 1 hour and 36 minutes = 1.6 hours. The distance from the start to the catching point is 45*1.6 = 72 miles. ANSWER

Solved.

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

The cyclist, traveling at 20mph for 2 hours before the car starts, has a head start of 40 miles.

Once the car starts, the difference between the speeds of the car and the cyclist is 45-20 = 25mph.

The number of hours the car will take to overtake the cyclist is equal to the DIFFERENCE in the distances divided by the DIFFERENCE in the speeds:

40/25 = 8/5 = 1.6

The car traveling 8/5 hours at 45mph will travel (8/5)(45)=(8)(9)=72 miles

ANSWER: The care will overtake the cyclist 72 miles from the starting point.

Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

A car traveling at 45 mph overtakes a cyclist who, riding at 20 mph, had a 2-hour head start. How far from the starting point does the car overtake the cyclist?

Let distance from starting point be D Then time taken for the car and bike to get to the meeting point = , respectively With the car taking 2 hours less to get to meeting point, we get the following TIME equation: 4D = 9D - 360 ------ Multiplying by LCD, 180 4D - 9D = - 360 - 5D = - 360 Distance from the starting point, where the bike was overtaken, or

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