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?

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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) About Me  (Show Source):
You can put this solution on YOUR website!
.

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    = 40%2F25 = 8%2F5  hours = 1 3%2F5  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) About Me  (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) About Me  (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 = matrix%281%2C3%2C+D%2F45%2C+and%2C+D%2F20%29, respectively
With the car taking 2 hours less to get to meeting point, we get the following TIME equation: matrix%281%2C3%2C+D%2F45%2C+%22=%22%2C+D%2F20+-+2%29
     4D = 9D - 360 ------ Multiplying by LCD, 180
4D - 9D = - 360
   - 5D = - 360
Distance from the starting point, where the bike was overtaken, or