Question 1139188
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An algebraic solution....<br>
let x be the speed he rode at
Then x+18 is the speed he could have ridden at<br>
The times to go 120 miles at the two speeds are 120/x and 120/(x+18).<br>
The problem says the time would be 15 hours less at the higher speed:<br>
{{{120/x-120/(x+18) = 15}}}
{{{120(x+18)-120x = 15x(x+18)}}}
{{{8(x+18)-8x = x(x+18)}}}
{{{144 = x^2+18x}}}
{{{x^2+18x-144 = 0}}}
{{{x+24)(x-6) = 0}}}
x = -24 (nonsense) or x = 6<br>
His actual speed was 6mph.  (A very slow bicycle speed!)<br>
CHECK:
120/6 = 20
120/(6+18) = 120/24 = 5
20-5 = 15<br>
An informal solution -- if algebra is not required....<br>
Make a list of pairs of numbers whose product is 120 and find two pairs that meet the conditions of the problem.<br>
1*120
2*60
3*40
4*30
5*24
6*20
8*15
10*12<br>
The pairs 5*24 and 6*20 satisfy the given conditions: 6+18 = 24; 20-5 = 15.