SOLUTION: brice left home and ran to school at 10 mi/hr. he ran back at 8 mi/hr. the entire trip took 27 min. How far did he run? Make a chart

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Question 166507: brice left home and ran to school at 10 mi/hr. he ran back at 8 mi/hr. the entire trip took 27 min. How far did he run? Make a chart
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The goal of this problem is to find the distance "d" of d=rt


Let t=time it took to get to school


So this means that it took 27-t minutes to get home


Now convert 10 mi/hr to mi/min to get 10%2F60=1%2F6 mi/min. So going to school, he's running 1%2F6 mi/min (or in decimal form 0.1667 mi/min)


Now convert 8 mi/hr to mi/min to get 8%2F60=2%2F15 mi/min. So coming home, he's running 2%2F15 mi/min (or in decimal form 0.1333 mi/min)
DirectionDistanceRate/SpeedTime
Going to Schoold miles1/6 mi/mint min
Coming Homed miles2/15 mi/min27-t min



Going to School:

d=rt Start with the distance rate time formula


d=%281%2F6%29t Plug in r=1%2F6

------------------

Coming Home:

d=rt Start with the distance rate time formula


d=%282%2F15%29%2827-t%29 Plug in r=8 and replace "t" with 27-t


%281%2F6%29t=%282%2F15%29%2827-t%29 Now plug in d=%281%2F6%29t (the "going to school" equation)


5t=4%2827-t%29 Multiply both sides by the LCD 30 to clear out the fractions.


-----------------------------------

5t=108-4t Distribute.


5t%2B4t=108 Add 4t to both sides.


9t=108 Combine like terms on the left side.


t=%28108%29%2F%289%29 Divide both sides by 9 to isolate t.


t=12 Reduce.


So he took 12 minutes to get to school.


d=%281%2F6%29t Go back to the first equation


d=%281%2F6%29%2812%29 Plug in t=12


d=12%2F6 Multiply


d=2 Reduce


So the distance from his home to school is 2 miles. Now since he went to school and came home he traveled that distance twice. So this means that he traveled a total distance of 4 miles