SOLUTION: Please help me solve this problem: Kathy and Gilbert drove a total of 892 miles in 16.4 hours. Kathy drove the first part of the trip and averaged 45 mph. Gilbert drove the remain

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Question 913953: Please help me solve this problem:
Kathy and Gilbert drove a total of 892 miles in 16.4 hours. Kathy drove the first part of the trip and averaged 45 mph. Gilbert drove the remainder of the trip and averaged 65 mph. For what length of time did Kathy drive?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
y and Gilbert drove a total of 892 miles in 16.4 hours.
Kathy drove the first part of the trip and averaged 45 mph.
Gilbert drove the remainder of the trip and averaged 65 mph.
For what length of time did Kathy drive?
:
let k = length of time Kathy drove
the total travel time was 16.4 hrs, therefore
(16.4-k) = length of time Gilbert drove
:
Write a distance equation; dist = speed * time
:
Kathy's dist + Gil's dist = 892 mi
45k + 65(16.2-k) = 892
45k + 1066 - 65k = 892
45k - 65k = 892 - 1066
-20k = -174
k = -174/-20
k = 8.7 hrs driven by Kathy
:
:
:
Check this; find the actual dist each drove. Gil drove; 16.4-8.7 = 7.7 hrs
65 * 7.7 = 500.5 mi driven by Gil
45 * 8.7 = 391.5 mi driven by Kathy
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total dist: 892 mi