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A cyclist bikes x distance at 10 miles per hour and returns [#permalink]

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12 Oct 2009, 13:02

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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?

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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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

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: A cyclist bikes x distance at 10 miles per hour and returns [#permalink]

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07 Jan 2014, 11:20

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Re: A cyclist bikes x distance at 10 miles per hour and returns [#permalink]

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05 Nov 2016, 15:59

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Re: A cyclist bikes x distance at 10 miles per hour and returns [#permalink]

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06 Nov 2016, 03:24

timmaxwell8 wrote:

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 x = 40 ( LCM of 10 & 8 )

So, Time taken for onward journey = 4 hrs And, Time taken for return journey = 5 hrs

So, total time taken = 9 hrs

Hence, average speed = 2*40/9 => 8.89 Hrs Thus, answer will be (D) 8.9 hours..

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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

We can use the formula average speed = total distance/total time. Since the distance for each leg traveled is x, the total distance is 2x, the time going is x/10, and the time coming back is x/8. We have:

average = 2x/(x/10 + x/8)

average = 2x/(4x/40 + 5x/40)

average = 2x/(9x/40)

average = (2x)(40/9x)

average = 80/9 = 8.9

Answer: D
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Re: A cyclist bikes x distance at 10 miles per hour and returns [#permalink]

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13 Aug 2017, 12:56

timmaxwell8 wrote:

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

This is clearly a round trip question so we should consider the formula

Total Distance= AvgSpeed * Time Spent

And also that

Distance1= Distance2 (we hold the distance constant because of course the distance on each trip is obviously the same)