Question 1193694: Cameron went on a bike ride of 40 miles. He realized that if he had gone 8 mph faster, he would have arrived 16 hours sooner. How fast did he actually ride?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! If you are really stuck, try setting up a data table based on RT=D.
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SPEEDS TIMES DISTANCE
HOW HE DID r 40
WHAT IF r+8 40
DIFFERENCE 16
This and what to do with it should be clear enough. Fill in what is missing and form the equation needed, and then solve.
Answer by ikleyn(52778)  (Show Source):
You can put this solution on YOUR website! .
The number of 40 has two divisors, 10 and 2, that differ by 8 units and such that if you divide 40 by 10 one time
and divide 40 by 2 next time, you will get two quotients, 4 and 20, that differ exactly 16 units.
By making this mental thought experiment, you quickly will get the answer to your question, without using any equations and much faster.
ANSWER. The slower rate is 2 miles per hour.
Solved.
Good as a mental exercise . . .
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
Formally, you would set this problem up by writing an equation that says the difference between 40 miles at the actual rate and 40 miles at a rate 8mph faster is 16 hours.
x = actual rate; 40/x = actual time
x+8 = other rate; 40/(x+8) = other time
Solve by multiplying through by the common denominator and solving the resulting quadratic equation.
But I agree with tutor @ikleyn that the way to get the most benefit from working this problem is to solve it using logical reasoning and simple mental arithmetic.
I will expand on her idea a bit to help you see how to find the solution.
The distance is an integer; and the differences in rates and times are integers. That means the solution is almost certainly in integers.
So look at the possible whole numbers of rates and times for which distance (rate * time) is 40 miles; then look for two of the times that differ by the required 16 hours.
rate time
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1 40
2 20
4 10
5 8
8 5
10 4
20 2
40 1
There are only two times in that list that have a difference of 16 hours: 20 and 4. Check to see that the difference in rates for those two times is the required 8mph.
40 miles in 20 hours = 2mph; 40 miles in 4 hours = 10mph; 10-2 = 8.
ANSWER: The actual rate is 2mph (almost impossibly slow for riding a bike!)....
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