SOLUTION: On the first part of a 363-mile trip, Emily averaged 58 miles per hour. Due to increased traffic volume, she averaged only 52 miles per hour on the last part of the trip. Find the

Question 155437This question is from textbook Algebra and Trigonometry
: On the first part of a 363-mile trip, Emily averaged 58 miles per hour. Due to increased traffic volume, she averaged only 52 miles per hour on the last part of the trip. Find the amount of time she traveled at each of the speeds if her total time for the trip was 6 hours and 45 minutes? This question is from textbook Algebra and Trigonometry

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Info from problem:
total miles: 363 miles
two speeds: 58 mph and 52 mph
total time: 6 hrs 45 mins OR 6.75 hrs
.
You must apply the "distance formula":
d = rt
where
d is distance
r is rate or speed
t is time
.
"distance traveled at 58 mph" + "distance traveled at 52 mph" = "total distance"
.
If we:
Let t = time traveling at 58 mph
then
6.75-t = time traveling at 52 mph
.
"distance traveled at 58 mph" = 58t
"distance traveled at 52 mph" = 52(6.75-t)
"total distance" = 363 miles
.
So, now we can rewrite:
"distance traveled at 58 mph" + "distance traveled at 52 mph" = "total distance"
as
58t + 52(6.75-t) = 363
58t + 351 - 52t = 363
6t + 351 = 363
6t = 12
t = 2 hours (time traveling at 58 mph)
.
6.75-t = 6.75-2 = 4.75 hours (time traveling at 52 mph)

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