Question 1193694
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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.<br>
x = actual rate; 40/x = actual time
x+8 = other rate; 40/(x+8) = other time<br>
{{{(40/x)-40/(x+8)=16}}}<br>
Solve by multiplying through by the common denominator and solving the resulting quadratic equation.<br>
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.<br>
I will expand on her idea a bit to help you see how to find the solution.<br>
The distance is an integer; and the differences in rates and times are integers.  That means the solution is almost certainly in integers.<br>
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.<br><pre>
  rate    time
 --------------
    1       40
    2       20
    4       10
    5        8
    8        5
   10        4
   20        2
   40        1</pre>
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.<br>
40 miles in 20 hours = 2mph; 40 miles in 4 hours = 10mph; 10-2 = 8.<br>
ANSWER: The actual rate is 2mph (almost impossibly slow for riding a bike!)....<br>