Question 1194434
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Get some good mental exercise by solving the problem informally.<br>
The distance is a whole number, the total time is a whole number, and the difference in speeds is a whole number.  So the two speeds are almost certain to be whole numbers.<br>
So look for two speeds that are whole numbers of miles per hour that differ by 4 and for which the total time going 24 miles and returning is 5 hours.  A little trial and error should quickly find speeds of 12 and 8 mph: {{{24/12+24/8 = 2+3 = 5}}}.<br>
ANSWERS: 12mph going; 8mph returning<br>
With formal algebra....<br>
Let x be his speed going
Then x-4 is his speed returning<br>
The total time for 24 miles each way is 5 hours:<br>
{{{24/x+24/(x-4)=5}}}<br>
Multiply by the common denominator, x(x-4):<br>
{{{24(x-4)+24(x)=5(x)(x-4)}}}
{{{24x-96+24x=5x^2-20x}}}
{{{5x^2-68x+96=0}}}
{{{(x-12)(5x-8)=0}}}<br>
{{{x=12}}} or {{{x=8/5}}}<br>
x=8/5 makes no sense, since it would make the return trip at a negative speed; so x=12.<br>
ANSWERS:
going: x=12mph
returning: x-4=8mph<br>