<PRE><B>Question 875439</B>
Trip to destination:



d = r*t



600 = r*t



600/r = t



t = 600/r



It takes 600/r hours to travel to the destination.



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Return Trip:



d = r*t



d = (r-10)*t



600 = (r-10)*t



600/(r-10) = t



t = 600/(r-10)



It takes 600/(r-10) hours to get back home.


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Add up the two times and set that equal to the total time 22



Time1 + Time2 = Total Time



600/r + 600/(r-10) = 22



Now we solve for r



600/r + 600/(r-10) = 22



r(r-10)*[ 600/r + 600/(r-10) ] = r(r-10)*22  ... multiply both sides by the LCD r(r-10) to clear out the fractions.



r(r-10)*[ 600/r ] + r(r-10)*[ 600/(r-10) ] = r(r-10)*22



(r-10)*600 + r*600 = r(r-10)*22 ... Notice how the fractions are gone after multiplying everything by the LCD



600(r-10) + 600r = 22r(r-10)



600r-6000 + 600r = 22r^2 - 220r



1200r-6000 = 22r^2 - 220r



0 = 22r^2 - 220r - 1200r + 6000



0 = 22r^2 - 1420r + 6000



22r^2 - 1420r + 6000 = 0



2(11r-50)(r-60) = 0



11r-50 = 0 or r-60 = 0



11r = 50 or r = 60



r = 50/11 or r = 60



r = 4.54545 or r = 60



If r = 4.54545, then r-10 = 4.54545-10 = -5.45455



It makes no sense to have a negative speed. So we ignore the solution r = -5.45455



The only practical solution is r = 60



Because r = 60, r-10 = 60-10 = 50



So the speed on the way to the destination was 60 mph. The speed coming back was 50 mph.
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