SOLUTION: A girl goes up a ski lift at 4 mph, and comes down the ski slope at 24 mph. If the ski slope is the same length as the ski lift, and you ignore any time spent at the top, her ave

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Question 256388: A girl goes up a ski lift at 4 mph, and comes down the ski slope at 24 mph. If the
ski slope is the same length as the ski lift, and you ignore any time spent at the
top, her average speed for the round trip, in miles per hour is a/b where a and b
are relatively prime. What is the value of (a+b)?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A girl goes up a ski lift at 4 mph, and comes down the ski slope at 24 mph.
If the ski slope is the same length as the ski lift, and you ignore any time spent at the top, her average speed for the round trip, in miles per hour is a/b where a and b are relatively prime.
What is the value of (a+b)?
:
Write a distance time equation: time = dist/speed
:
Let d = the one-way distance
:
Up time + down time = total time
d%2F4 + d%2F24 = %282d%29%2F%28a%2Fb%29
Invert the dividing fraction and multiply
d%2F4 + d%2F24 = %282db%29%2Fa
Simplify, divide thru by d
1%2F4 + 1%2F24 = %282b%29%2Fa
Multiply by 24a to get rid of the denominators. results
6a + a = 24(2b)
:
7a = 48b
a = 48%2F7b
:
The integer solution, b=7, then a=48; these are relatively prime aren't they?
7 + 48 = 55; (a+b)
:
Average speed: 48%2F7 = 6.587 mph, seems reasonable
:
Let me know if screwed this one up, please; ankor@att.net