SOLUTION: 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 num

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 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 num      Log On


   

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) About Me  (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)