Question 184212: During a work-out session, Mark either ran at a speed of 7MPH or walked at a speed of 3MPH. He completed 20 miles in 3 hours. Please help me.
1. Let r represent the number of miles Mark ran and w respresent the number of miles Mark walked. Write a system of equations that represents the situation.
2.Solve the system of equations to find how much time Mark spent running.
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! the total distance is 20 mi, so r+w=20 ... and w=20-r
the total time is 3 hr ... since rate times time equals distance, time equals distance divided by rate
(r/7)+(w/3)=3
substituting ... (r/7)+((20-r)/3)=3
subtracting 20/3 ... (r/7)-(r/3)=-11/3
multiplying by 21 (LCD) ... 3r-7r=-77 ... -4r=-77
dividing by -4 ... r=77/4
since time equals distance divided by rate, Mark's running time is (77/4)/7 or 11/4 hr (2hr45min)
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