SOLUTION: The average speed of a car is three times as fast as the average speed of a cyclist. To travel 225 km, the cyclist requires 5 h more than the car. Determine the average speed of th

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Question 1148982: The average speed of a car is three times as fast as the average speed of a cyclist. To travel 225 km, the cyclist requires 5 h more than the car. Determine the average speed of the cyclist and the car.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let "x" be the average speed of the cyclist, in kilometers per hour.


Then the average speed of the car is  3x km/h.


The time equation, from the condition, is


    225%2Fx - 225%2F%283x%29 = 5  hours.


To solve it, multiply both sides by 3x.  You will get


    675 - 225 = 15x

    450       = 15x

      x       = 450/15 = 30.


ANSWER.  The cyclist's average speed is  30km/h.  The car's average speed is 3*30 = 90 km/h.


CHECK.   225%2F30 - 225%2F90 = 15%2F2 - 15%2F6 = 15%2F2 - 5%2F2 = 10%2F2 = 5 hours.   ! Correct !

Solved.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor has shown a perfectly good method for solving the problem.

Here is a completely different alternative method.

This alternative is in no way any "better" than the other; it simply shows you that there are (nearly always) many different ways for setting up problems to be solved.

If you want to be good at solving problems, you should understand how both methods are valid.

The speed of the car is 3 times the speed of the cyclist.

Since the distances are the same, the time required by the cyclist is 3 times the time required by the car.

Let the time for the car be x; then the time for the cyclist is 3x.

The difference between the times is 2x; and we know that difference is 5 hours.

2x=5
x+=+2.5

The time for the car is x=2.5 hours; the time for the cyclist is 3x = 7.5 hours.

The distance is 225km; so the speed of the car is 225/2.5 = 90km/hr, and the speed of the cyclist is 225/7.5 = 30km/hr.