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A cyclist bikes x distance at 10 miles per hour and returns

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A cyclist bikes x distance at 10 miles per hour and returns [#permalink] New post 12 Oct 2009, 12:02
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A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?

A. 8.1
B. 8.3
C. 8.6
D. 8.9
E. 9.0
[Reveal] Spoiler: OA
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Re: Average rate on round trip [#permalink] New post 12 Oct 2009, 12:16
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timmaxwell8 wrote:
18. A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?

A. 8.1
B. 8.3
C. 8.6
D. 8.9
E. 9.0


Let the distance be 40 miles (40 because it's divisible by 10 and 8)

Time for 1st trip=40/10=4 hours
Time back =40/8=5hours

Average rate=total distance/total time=(40+40)/(4+5)=80/9=8.9

D.

It's possible to write the formula with variable x for distance but the above way is fastest.

Here is the formula if you need it:
Av rate=(x+x)/(x/10+x/8)=80/9=8.9
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Re: Average rate on round trip [#permalink] New post 12 Oct 2009, 21:12
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total distance = 2x
Time on the way there is (x miles)/(10 miles/hour)= x/10 hours
Time on the way back is (x miles)/(8 miles/hour)= x/8 hours
Total time=(x/10)+(x/8)=(9x/40) hours

Average rate=(total distance)/(total time)
x is a dummy variable and will cancel out
Average rate=(2x)miles/(9x/40)hour= 80/9 mph=8.9 mph D
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Re: Average rate on round trip [#permalink] New post 13 Oct 2009, 13:24
Pick numbers that make sense. 8x10--> 80 miles

1st Trip takes 8 hours at 10/mph
2nd Trip takes 10 hours at 8/mph

160/18
= 8.9mph
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Re: Average rate on round trip [#permalink] New post 02 Jan 2010, 13:15
Another approach to roundtrip average rates is to conceptually utilize weighting. Because time is a weight here, slightly more time, or weight, is used at 8 mph than 10 mph, so the average rate should be slightly closer to 8 mph than it is to 10 mph. Answer 8.9 mph.

Phew...I finally made my first post.
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Re: Average rate on round trip [#permalink] New post 17 Apr 2011, 12:17
the avg speed formula does the trick ...
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Re: Average rate on round trip [#permalink] New post 17 Apr 2011, 20:54
2x/(x/10 + x/8)

= 2/(1/10 + 1/8)

= 2 * 40/(4 + 5)

= 80/9 = 8.88 ~ 8.9


Answer - D
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Re: Average rate on round trip [#permalink] New post 17 Apr 2011, 23:01
Substitute a number in for X

RT=D

R T D
--------------------------------
a 10 40
b 8 40

I chose the common multiple 40, so now since average rate = total distance/total time we need to find time

rt=d --? t=d/4

so


R T D
--------------------------------
a 10 4 40
b 8 5 40
---------------------------------------
total 9 80

r=80/9

r=8.888888 --> ~8.9 so D is the answer
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Re: A cyclist bikes x distance at 10 miles per hour and returns [#permalink] New post 07 Jan 2014, 10:20
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Re: A cyclist bikes x distance at 10 miles per hour and returns   [#permalink] 07 Jan 2014, 10:20
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