SOLUTION: Please could you help me with this question: "Sarah goes up a hill and then down again the same way.On the way up she averages 2 miles per hour. On the way down she averages 4 mi

Question 830352: Please could you help me with this question:
"Sarah goes up a hill and then down again the same way.On the way up she averages 2 miles per hour. On the way down she averages 4 miles per hour. What is Sarah's average speed in miles per hour for the whole journey?"
I know that the answer is 2.6 miles per hour but I'm not sure how to work it out.
Thank You
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
x time up
y time down
d one-way distance up or down

________________speed___________time________________distance
up hill_________2________________x__________________d
down hill_______4________________y__________________d
Total?________________________x+y__________________2d

The relationship of speeds means you can make a relationship of the times.
Twice as fast down the hill means HALF the time as up the hill:

________________speed___________time________________distance
up hill_________2________________x__________________d
down hill_______4________________x/2__________________d
Total?________________________(3/2)x__________________2d

Can we find expressions for d?

________________speed___________time________________distance
up hill_________2________________x__________________d=2x
down hill_______4________________x/2__________________d=4(x/2)
Total?________________________(3/2)x__________________2d=4x

SPEED is distance divided by time:
We want total distance and total time.
mph.
This is a little greater than what value you expected.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

Please could you help me with this question:
"Sarah goes up a hill and then down again the same way.On the way up she averages 2 miles per hour. On the way down she averages 4 miles per hour. What is Sarah's average speed in miles per hour for the whole journey?"
I know that the answer is 2.6 miles per hour but I'm not sure how to work it out.
Thank You

Average speed = total distance � total time
Let distance, one-way be D
Total distance:
Time uphill:
Time downhill:
Total time for entire journey: , or , or
Average speed = � , or , or , or mph
You can do the check!!
If you need a complete and detailed solution, let me know!!
Send comments, �thank-yous,� and inquiries to �D� at MathMadEzy@aol.com.
Further help is available, online or in-person, for a fee, obviously.
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