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?

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(39618) (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:

AND

Solve that system for g and k.
RELATED QUESTIONS
Kathy and Gilbert drove a total of 337 miles in 8 hours. Kathy drove the first part of... (answered by josgarithmetic)

Please help me solve this problem: Kathy and Gilbert drove a total of 892 miles in 16.4... (answered by ankor@dixie-net.com)

Les and Gil drove a total of 733 miles in 11.6 hours. Les drove the first part of the... (answered by checkley77)

Chris and Gilbert drove a total of 522 miles in 8.2 hours. Chris drove the first part of... (answered by ewatrrr)

Chris and Gilbert drove a total of 459 miles in 11.8 hours. Chris drove the first part of (answered by richwmiller)

Kathy and Jan drove a total of 497 miles in 10.4 hours. Kathy drove the first part of the (answered by checkley77)

Jan and Kathy drove a total of 534 miles in 12.8 hours. Jan drove the first part of the... (answered by ankor@dixie-net.com)

Angelina drove at an average rate of 80 kph and then stopped 20 minutes for gas. After... (answered by ankor@dixie-net.com)

A truck driver drove for 2 days. On the second day he drove for 3 hours longer and at an... (answered by ankor@dixie-net.com)