SOLUTION: As Kayla leaves the gym for a 12 mile run. She starts her run on level terrain where she can run at 8 miles per hour. Then her path becomes hilly and she can only run at 4 miles pe

Question 210731: As Kayla leaves the gym for a 12 mile run. She starts her run on level terrain where she can run at 8 miles per hour. Then her path becomes hilly and she can only run at 4 miles per hour. Find the amount of time she runs at each speeds if her total running time is 2 hours and 20 minutes.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
As Kayla leaves the gym for a 12 mile run. She starts her run on level terrain where she can run at 8 miles per hour. Then her path becomes hilly and she can only run at 4 miles per hour. Find the amount of time she runs at each speeds if her total running time is 2 hours and 20 minutes.
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Level DATA:
rate = 8 mph ; distance = x miles ; time = d/r = x/8 hrs.
----------------------
Hilly DATA:
rate = 4 mph ; distance = (12-x) miles ; time = (12-x)/4 hrs
-----------------------
Equation:
time + time = 2 1/3 hrs
x/8 + (12-x)/4 = 7/3
----
3x + 6(12-x) = 8*7
3x + 72 - 6x = 56
-3x = -16
x = 16/3 miles (distance run on the level)
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Time on level ground: (16/3)/8 = 2/3 hr.
Time on hilly ground: (7/3)-(2/3) = 4/3 hr.
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Cheers,
Stan H.
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