Question 279150: During a workout session, Mark either ran at a speed of 7 miles per hour or walked at a speed of 3 miles per hour. He completed 20 miles in 3 hours. Let r represent the number of miles Mark ran and w represent the number of miles Mark walked. Write a system of equations that represents the situation, and Solve the system of equations to find how much time Mark spent running.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! During a workout session, Mark either ran at a speed of 7 miles per hour or walked at a speed of 3 miles per hour. He completed 20 miles in 3 hours. Let r represent the number of miles Mark ran and w represent the number of miles Mark walked. Write a system of equations that represents the situation, and Solve the system of equations to find how much time Mark spent running.
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Walking DATA:
rate = 3 mph ; distance = r miles ; time = r mi/3 mph = (r/3) hrs.
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Running DATA:
rate = 7 mph ; distance = w miles ; time = w mi/7 mph = (w/7)hrs.
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Equations:
Distance: r + w = 20 miles
Time::::: (r/7) + (w/3) = 3 hrs
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Solve the system:
Multiply thru the Time Equation by 21:
Muliple thru the Distance Equation by 7:
7r + 7w = 140
3r + 7w = 63
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Subtract 2nd from 1st and solve for "r":
4r = 77
r = 19.25 mile (distance Mark ran)
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Mark's running time = [19.25 miles]/[7mph] = 2 hr 45 minutes ======================================
Cheers,
Stan H.
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