SOLUTION: A man finds that he can reach a certain town in 6 hours by traveling 240 miles on an interstate highway and then changing to local roads for 80 miles. He can also get there by trav

Question 1113774: A man finds that he can reach a certain town in 6 hours by traveling 240 miles on an interstate highway and then changing to local roads for 80 miles. He can also get there by traveling 270 miles on a different interstate then proceeding 40 miles on a local highway. This route saves 1/2 hour. If he averages x mph on interstates and y on local roads, find his average speed on the interstate and on local roads.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

By the first route, the time on interstates is 240/x and the time on local roads is 80/y; by the second route, the respective times are 270/x and 40/y.

The total time for the first route is 6 hours; for the second it is 5.5 hours.

(1) ;
(2)

Don't make the mistake of trying to get rid of the variables in the denominators -- the required work will be FAR harder than necessary. Solving the pair of equations in their current form is easy.

Multiply the second equation by 2 and subtract one equation from the other to eliminate y:

(3)
(4)

Substitute into either original equation to find y:

Answer: 60mph on interstates; 40mph on local roads.

Check...
1st route: 240/60+80/40 = 4+2 = 6
2nd route: 270/60+40/40 = 4.5+1 = 5.5
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