SOLUTION: This is a word problem and we have been using cramer's rule, but I don't know how to set it up. Rosa rides the bus to work. Usually she rides 35 min and then walks 6 min to get t

Question 105797This question is from textbook Algebra 2
: This is a word problem and we have been using cramer's rule, but I don't know how to set it up. Rosa rides the bus to work. Usually she rides 35 min and then walks 6 min to get to work. Since the bus travels at 30 miles per hour and her walking speed is 5 mph, she can easily determine that the total distance is 18 miles. One day when the weather was nice, she decides to get off the bus earlier and walk the rest of the way for exercise. She only has a total of 75 min to get to work, so she can't afford to get off the bus too early. How much time should she spend on the bus before getting off to walk? The answer is 28.2 min. I have been out of school due to medical reasons for over a month and I am trying to teach myself the math before I go back. If you can help me to figure out how to set this up I would really appreciate it. This question is from textbook Algebra 2

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I don't know how to set it up. Rosa rides the bus to work. Usually she rides 35 min and then walks 6 min to get to work. Since the bus travels at 30 miles per hour and her walking speed is 5 mph, she can easily determine that the total distance is 18 miles.
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The above data allows you to figure out the distance from home to work:
Ride DATA:
Time = (35/60) hr ; Rate = 30 mph ; Distance = rt = (35/60)30 = 17.5 miles
--
Walk DATA:
Time = (6/60) hr ; Rate = 5 mph ; Distance = rt = (6/60)5 = (1/2) mile
--
So, distance from home to work is 17.5+0.5 = 18 miles
=========================
One day when the weather was nice, she decides to get off the bus earlier and walk the rest of the way for exercise. She only has a total of 75 min to get to work, so she can't afford to get off the bus too early. How much time should she spend on the bus before getting off to walk? The answer is 28.2 min.
The above data gives you an equation for the distance from home to work:
Ride DATA:
Time = (x/60) hr ; Rate = 30 mph ; Distance = rt = (x/60)30 = (1/2)x miles
--
Walk DATA:
Time = (75-x)/60 hr ; Rate = 5 mph ; Distance = rt = [(75-x)/60]5 = (75-x)12 mi.
-----------
EQUATION:
2nd Total distance = 1st total distance
(1/2)x + (75-x)/12 = 18 miles
Multiply thru by 12 to get:
6x + 75-x = 12*18
5x = 141
x = 28.2 minutes
That is the amount of time she should ride to get to work in 75 minutes.
================
Cheers,
Stan H.
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