SOLUTION: A motorcycle travels 196 miles in the same amount of time that a car travels 161. The rate of the motorcycle is 10 miles per hour faster than the rate of the car. Find the rate of

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Question 1149262: A motorcycle travels 196 miles in the same amount of time that a car travels 161. The rate of the motorcycle is 10 miles per hour faster than the rate of the car. Find the rate of the car
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
r, car's speed

196%2F%28r%2B10%29=161%2Fr
-
196r=161r%2B1610
35r=1610
highlight%28r=46%29

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a very different method for solving the problem....

The ratio of the distances is 196/161 = 28/23.

Since the times are the same, the ratio of the speeds is also 28/23.

You want two speeds that are in that same ratio and differ by 10.

So look for a fraction equivalent to 28/23 in which the numerator is 10 more than the denominator.

In 28/23, the numerator is 5 more than the denominator.

So multiply numerator and denominator by 2 to find the rates of the two vehicles.

28/23 = 56/46

The rate of the car is 46mph; the rate of the motorcycle is 56mph.