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

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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) About Me  (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
45%2Fr+%2B+%2845%2F%283r%2F4%29%29=7%2F4

45%2Fr+%2B+%2860%2Fr%29=7%2F4


%2860%2B45%29%2Fr=7%2F4%29
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) About Me  (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
speed=distance%2Ftime <--> time%2Aspeed=distance <--> time=distance%2Fspeed

Measuring time in hours, it took 1%2B45%2F60=1.75=7%2F4 hours for the whole round trip.
The first part, at average speed r would have taken 45%2Fr hours.
The return trip, at average speed %283%2F4%29r would have taken 45%2F%28%283%2F4%29r%29 hours.
Adding up, we get one equation.
or 45%2Fr%2B45%2F%28%283%2F4%29r%29=1.75
and we can solve for r .

Solving:
45%2Fr%2B45%2F%28%283%2F4%29r%29=7%2F4
45%2Fr%2B%2845%2Fr%29%284%2F3%29=7%2F4
%2845%2Fr%29%281%2B4%2F3%29=7%2F4
%2845%2Fr%29%287%2F3%29=7%2F4
45%284%2F3%29=r
highlight%28r=60%29 and %283%2F4%29r=%283%2F4%2960=highlight%2845%29

USING SYSTEMS OF LINEAR EQUATIONS
x= time (in hours) Julie spent driving at an average speed of r miles per hour, while going wherever Julie was going.
y= time (in hours) Julie spent driving at an average speed of %283%2F4%29r miles per hour during the return trip.
Since time%2Aspeed=distance , for both parts of the trip we have
rx=45 and %283%2F4%29ry=45 ,
and we could combine them into
rx=%283%2F4%29ry --> x=%283%2F4%29y
We also know that x%2By=7%2F4

Solving:
system%28x=%283%2F4%29y%2Cx%2By=1.75%29 --> system%28x=%283%2F4%29y%2C%283%2F4%29y%2By=1.75%29 --> system%28x=%283%2F4%29y%2C%287%2F4%29y=7%2F4%29 --> system%28x=%283%2F4%29%2A1%2Cy=1%29 --> highlight%28system%28x=3%2F4%2Cy=1%29%29
So the average speed is 45%2F%28%283%2F4%29%29=45%2A%284%2F3%29=highlight%2860%29 on the way over there,
and 45%2F1=highlight%2845%29 for the return trip.