SOLUTION: A small company involved in a delivery business is in charge of two routes. A driver on route a travels 70 miles and a driver on route B travel 75 miles on a given day. The Driver

Question 30134: A small company involved in a delivery business is in charge of two routes. A driver on route a travels 70 miles and a driver on route B travel 75 miles on a given day. The Driver on route A travels 5 miles an hour slower than the driver on route B. Also the route A takes one half (1/2) hour longer than B. How fast is each driver traveling?
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
The equation for this problem is 75/S+.5=70/S-5. (S is the speed).
Cross multiplying we get 70S=75S-375+.5S~2-2.5S
70S=72.5S-375+.5S~2
0=72.5S-70S-375+.5S~2
0=2.5S-375+.5S~2
0=.5S~2+2.5S-375

Dividing all terms by .5 we get s~2+5s-750=0. Factoring 750 to get a difference of 5 we get 25 & 30. Therefore the factors of this equation are:
(S+30)(S-25)=0 Or S=-30 & S=+25. The answer is 25 miles per hour for route B & 5 miles less for route A or 20 miles per hour. Route B goes 75 miles in 3 hours 75/25 while route A goes 70 miles in in 3.5 hours or at a rate of 70/3.5 20 miles per hour.
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