SOLUTION: A man rode his bicycle 90 miles. If he had traveled 2/11 mile more per hour, he would have made the trip in ten minutes less time. How long did the trip last?

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Question 1116402: A man rode his bicycle 90 miles. If he had traveled 2/11 mile more per hour, he would have made the trip in ten minutes less time. How long did the trip last?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The tutor @MathTherapy correctly noticed that there was a mistake in my previous solution to this problem.

            So I re-edit the solution.  Now what you see below is correct and corrected.

            Thanks to @MathTherapy ! 


Let "t" be the time under the hypothetical scenario, in hours (the "if . . . " scenario).


Then your "speed" equation is this

90%2Ft - 90%2F%28t%2B1%2F6%29 = 2%2F11.    (1)


In this equation

    90%2F%28t%2B1%2F6%29 is the regular speed (the basic scenario);

    90%2Ft is the hypothetical speed (the "if . . . " scenario).

    2%2F11 is the given difference of speeds;  1%2F6 = 1%2F6 of an hour = 10 minutes.


Simplify eq(1):

90%2Ft - 540%2F%286t%2B1%29 = 2%2F11


11*90*(6t+1) - 11*540*t = 2*t*(6t+1)


990 = 12t^2 + 2t,


12t^2 + 2t - 990 = 0


t%5B1%2C2%5D = %28-2+%2B-+sqrt%282%5E2+%2B+4%2A12%2A990%29%29%2F%282%2A12%29 = %28-2+%2B-+218%29%2F24.


The only positive solution  is  t = %28-2+%2B+218%29%2F24 = 216%2F24 = 9 hours.


Thus, the hypothetical scenario time is 9 hours, which means that the regular scenario time is 9 hours and 10 minutes.


Answer.  9 hours and 10 minutes.

Solved.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A man rode his bicycle 90 miles. If he had traveled 2/11 mile more per hour, he would have made the trip in ten minutes less time. How long did the trip last?
Time trip took: