SOLUTION: Kathy and Gilbert drove a total of 568 miles in 11 hours. Gilbert drove at an average of 45mph and Kathy drove at an average of 55mph. How long did Gilbert drive?

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Question 730589: Kathy and Gilbert drove a total of 568 miles in 11 hours. Gilbert drove at an average of 45mph and Kathy drove at an average of 55mph. How long did Gilbert drive?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let g = hours that Gilbert drove. Let k = hours that Kathy drove.

Driver_________rate_____________time______________distance
Gilbert________45_______________g_________________45*g
Kathy__________55_______________k_________________55*k
TOTAL___________________________11________________568

Deciding to use two variables was tricky. I know of no formal method to decide to choose those two variables, g and k, for the drive time of each driver. The data as arranged indicates the obvious system of two equations:

SYSTEM:
highlight%28g%2Bk=11%29
AND
highlight%2845g%2B55k=568%29
Solve that system for g and k.