SOLUTION: Please help me solve this applying systems of linear equations word problem! Julie drove her car for 45 miles at an average speed of r miles per hour. On the return trip, traffic

Question 831042: Please help me solve this applying systems of linear equations word problem! Julie drove her car for 45 miles at an average speed of r miles per hour. On the return trip, traffic has increased, and Julie average speed is 3/4r. The round trip took a total of 1 hour and 45 minutes. Find the average speed for each portion of the trip. Thanks
Found 2 solutions by mananth, KMST:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
t=d/r
time going = 45/r
time return =45/(3r/4)
Time going + time return = 7/4 hours

105/r =7/4
r= 4*105/7

r=60
speed while going = 60 mph
returning speed = 3/4 *60 = 45 mph

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I do not see that problem as an "applying systems of linear equations word problem", but I will try to do it that way, and also show you an alternate way.

THE MORE DIRECT WAY:
Average speed, time, and distance are related by
<--> <-->

Measuring time in hours, it took hours for the whole round trip.
The first part, at average speed would have taken hours.
The return trip, at average speed would have taken hours.
Adding up, we get one equation.
or
and we can solve for .

Solving:

and

USING SYSTEMS OF LINEAR EQUATIONS
= time (in hours) Julie spent driving at an average speed of miles per hour, while going wherever Julie was going.
= time (in hours) Julie spent driving at an average speed of miles per hour during the return trip.
Since , for both parts of the trip we have
and ,
and we could combine them into
-->
We also know that

Solving:
--> --> --> -->
So the average speed is on the way over there,
and for the return trip.
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