SOLUTION: During my trip to work, I spent 3/4 of the time driving on the highway, during which I covered 5/6 of the distance. My average speed on the highway was 60 miles per hour. What are

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Question 766839: During my trip to work, I spent 3/4 of the time driving on the highway, during which I covered 5/6 of the distance. My average speed on the highway was 60 miles per hour. What are the possible values of my average speed, in miles per hour, during the time I was not on the highway?
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
h is total time
d is total distance
ROAD______________speed_______time___________distance
Highway___________60_________(3/4)h_________(5/6)d
NonHighway________(___)______(1/4)h_________(1/6)d

ROAD______________speed_______time___________distance
Highway___________60_________(3/4)h_________(5/6)d
NonHighway________(r)______(1/4)h_________(1/6)d

Try making two equations using rate times time equals distance:
and ; this last equation gives an expression for unknown r.


But we still have three variables and two equations, just one is rearranged.

This seems an open-ended problem. Use the highway equation to eliminate either the h or the d in the r equation. You might want to pick an arbitrary value for h or d.
Work with the highway equation....

So you can form the equation


No longer seems so open-ended. Solution method felt strange, but result is very clear.
With that result r=36 mph, you can evaluate possible averages of highway and nonhighway speeds.

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