SOLUTION: I can not come up with how to do the following, could you please please help me? On the first part of a 317 mile trip a salesperson averaged 58 mph. The salesperson averaged only

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Question 601637: I can not come up with how to do the following, could you please please help me?
On the first part of a 317 mile trip a salesperson averaged 58 mph. The salesperson averaged only 52 mph on the last part of the trip. The total time of the trip was 5hrs 45 min. Find the amount of time at each of the 2 speeds?
Any help would be greatly appreciated, for some reason I can not even figure how to set the problem up. Thanks in advance.
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
On the first part of a 317 mile trip a salesperson averaged 58 mph. The salesperson averaged only 52 mph on the last part of the trip. The total time of the trip was 5hrs 45 min. Find the amount of time at each of the 2 speeds?
.
We're going to apply the "formula" of d=rt
.
Converting 5hrs 45 min to hours we get:
5.75 hours (total time traveled)
.
Let t = time (hours) traveled at 58 mph
then
5.75-t = time (hours) traveled at 52 mph
.
58t + 52(5.75-t) = 317
58t + 299-52t = 317
6t + 299 = 317
6t = 18
t = 3 hours (time traveled at 58 mph)
.
time traveled at 52 mph:
5.75-t = 5.75-3 = 2.75 hours (or, 2 hours 45 minutes)