SOLUTION: Cabrina and Dabney are attending a conference. After the conference, Cabrina drives home to Boise at an average speed of 75 mph and Dabney drives home to Portland at an average spe

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Question 196209: Cabrina and Dabney are attending a conference. After the conference, Cabrina drives home to Boise at an average speed of 75 mph and Dabney drives home to Portland at an average speed of 60 mph. If the sum of their driving time is 11.3 hours and the sum of distance driven is 783 miles, determine the time each woman spent driving home.
Answer by ankor@dixie-net.com(22740) (Show Source):
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Cabrina and Dabney are attending a conference. After the conference, Cabrina
drives home to Boise at an average speed of 75 mph and Dabney drives home to
Portland at an average speed of 60 mph. If the sum of their driving time is
11.3 hours and the sum of distance driven is 783 miles,
determine the time each woman spent driving home.
:
Let t = C's driving time
It states the sum of their times is 11.3, therefore:
(11.3 - t) = D's driving time
;
:
The sum of their distances is given as 783 mi, write distance equation:
Dist = speed * time
:
C's dist + D's dist = 783 mi
75t + 60(11.3 - t) = 783
:
75t + 678 - 60t = 783
:
75t - 60t = 783 - 678
:
15t = 105
t=
t = 7 hrs is C's driving time
and
11.3 - 7 = 4.3 hrs is D's driving time
:
:
Check solutions by finding the sum of the distances
75(7) + 60(4.3) =
525 + 258 = 783, confirms our solutions