SOLUTION: The horse galloped m miles at p miles per hour and then trotted m miles at k miles per hour. What was the average speed for the entire trip?

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Question 551178: The horse galloped m miles at p miles per hour and then trotted m miles at k miles per hour. What was the average speed for the entire trip?
Found 3 solutions by ankor@dixie-net.com, nyc_function, solver91311:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The horse galloped m miles at p miles per hour and then trotted m miles at k miles per hour.
What was the average speed for the entire trip?
:
let a = the average speed of the entire trip
:
m%2Fp + m%2Fk = %282m%29%2Fa
:
%28mk%2Bmp%29%2F%28pk%29 = %282m%29%2Fa
Cross multiply
a(mk+mp) = (pk*2m)
a = %28%282pkm%29%29%2F%28%28mk%2Bmp%29%29
cancel out m
a = %28%282pk%29%29%2F%28%28k%2Bp%29%29 the average speed for the entire trip

Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
If m = pt, then (m/t) = p.

If m = kt, then (m/t) = k.

Average speed for the entire trip = p + k.

Substitute and add.

(m/t) + (m/t) = 2m/t.

I hope this helps.




Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Average speed is total distance divided by total time.

Time is distance divided by rate. So the time for the gallop part of the trip is:



and the time for the trot part of the trip is:



And then the total time is:



Then since the total distance is , the average speed is:



John

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