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

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)
RELATED QUESTIONS
During a workout session, Mark either ran at a speed of 7 miles per hour or walked at a... (answered by stanbon)

A man travelled from one city to another city by foot he covered 25km by foot in 3... (answered by ankor@dixie-net.com)

A man walked to the next town at the rate of 3 miles per hour and rode back in a bus... (answered by josgarithmetic)

the tables shows data from 4 cyclists during a training session. If Raul rode at a... (answered by ikleyn)

Bryce ran a 4 mile race at a constant speed of 10 mph. Conner left at the same time and... (answered by lwsshak3)

Sarah ran 5 miles at a constant speed. She then reduces her speed by 3 miles per hour and (answered by josgarithmetic)

Vernon ran a 100 meter race at an average speed of t meters per second. He completed the... (answered by Alan3354)

Kayaker takes 3 hours to cover distance of 30 miles downstream. It takes 5 hours to... (answered by dkppathak,ikleyn)

A car completed a 1000 mile race in 35 hours. For the 600 miles traveled driving... (answered by scott8148,edjones)