SOLUTION: Max runs the first km of her training session at 8km/h. At least how many kilometers must she run at 15 km/h in order to average 12km/h for the whole session?

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Question 100921: Max runs the first km of her training session at 8km/h. At least how many kilometers must she run at 15 km/h in order to average 12km/h for the whole session?
Answer by ankor@dixie-net.com(12692) About Me  (Show Source):
You can put this solution on YOUR website!
Max runs the first km of her training session at 8km/h. At least how many kilometers must she run at 15 km/h in order to average 12km/h for the whole session
:
Time = distance/speed
:
Let d = distance required at 15 km/h to average 12km/h
:
Write a time equation
Time at 8 km/h + time at 15 km/h = time at 12/km/h
1%2F8 + d%2F15 = %28%28d%2B1%29%29%2F12
:
Multiply equation by 120 to get rid of the denominators
120*1%2F8 + 120*d%2F15 = 120*%28%28d%2B1%29%29%2F12
:
Cancel out the denominators:
15(1) + 8(d) = 10(d+1)
:
15 + 8d = 10d + 10
:
8d - 10d = 10 - 15
:
-2d = -5
:
d = + 5/2 or 2.5 km at 15 km/hr rate
:
Total distance would be 3.5 km
:
Check solution by calculating av speed = dist/time
:
Find the time:
1%2F8 + 2.5%2F15 =
1%2F8 + 1%2F6 =
3%2F24+ 4%2F24 = 7/24 hr, is the total time
:
Check average speed (dist/time)
7/2 (3.5) divided by 7/24
7%2F2 * 24%2F7 = 24/2 = 12 km/hr
:
Sorry, I got twisted around on the first attempt