SOLUTION: Cabrina and Dabney are attending a conference. After the​ conference, Cabrina drives home to Boise at an average speed of 55 miles per hour and Dabney drives home to Portland at

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Question 1159145: Cabrina and Dabney are attending a conference. After the​ conference, Cabrina drives home to Boise at an average speed of 55 miles per hour and Dabney drives home to Portland at an average speed of 40 miles per hour. If the sum of their driving times is 11.9 hours and if the sum of the distances driven is 566 ​miles, determine the time each woman spent driving home.
Found 2 solutions by josgarithmetic, Shin123:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x, the time for Cabrina
11.9-x, the time for Dabney

55x%2B40%2811.9-x%29=566-------------solve this.

Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say that Cabrina spent x hours driving home and Dabney spent y hours driving home. We have the equations:
system%28x%2By=11.9%2C55x%2B40y=566%29
Multiplying the first equation by 40 gives system%2840x%2B40y=476%2C55x%2B40y=566%29 Subtracting the first equation from the second gives 15x=90. Dividing both sides by 15 gives highlight%28highlight_green%28highlight%28x=6%29%29%29. Plugging this value into the second equation gives highlight%28highlight_green%28highlight%28y=5.9%29%29%29. So Cabrina drove for 6 hours and Dabney drove for 5.9 hours.