Question 1182960
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Of course you should understand the algebraic solution to the problem, as shown by the other tutor.<br>
However, if a formal algebraic solution is not required, and the speed of solving the problem is important -- as in a timed math competition -- you can find the answer by playing with numbers.<br>
There are several pairs of numbers -- hours and speed in mph -- that give a product of a distance of 504 miles.  Search for two such pairs in which the sum of the two hour numbers is 16 and the difference between the two speed numbers is 16.<br>
Ignore unreasonable pairs, such as 2 hours and 252mph....<br><pre>
  6 * 84
  7 * 72
  8 * 63
  9 * 56
 12 * 42</pre>
The two pairs that satisfy the conditions of the problem are 7*72 and 9*56.  The sum of the two hours numbers is 16, and the difference between the two speed numbers is 16.<br>
ANSWER: The two rates are 72 and 56 mph.<br>