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

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Joined: 08 Oct 2009
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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?

A. 8.1
B. 8.3
C. 8.6
D. 8.9
E. 9.0
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Posts: 54369
Re: Average rate on round trip  [#permalink]

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12 Oct 2009, 13:16
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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]

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12 Oct 2009, 22:12
1
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]

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13 Oct 2009, 14:24
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]

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02 Jan 2010, 14:15
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]

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17 Apr 2011, 13:17
the avg speed formula does the trick ...
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Re: Average rate on round trip  [#permalink]

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17 Apr 2011, 21:54
2x/(x/10 + x/8)

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

= 2 * 40/(4 + 5)

= 80/9 = 8.88 ~ 8.9

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Re: Average rate on round trip  [#permalink]

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18 Apr 2011, 00:01
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]

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

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10 Jul 2017, 02:19
the best way to solve avg speed when same distance is convered by two dift velocity

Avg speed = 2ab/a+b

so 2x10x8/18 =8.9 so answer is D
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Re: A cyclist bikes x distance at 10 miles per hour and returns  [#permalink]

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12 Jul 2017, 17:02
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

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

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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)

Now we can just plug in a simple value

40/8 = 5 hours

40/10= 4 hours

80miles= Avgspeed * 9 hours

80/9= 8.888888 so round up

D
Re: A cyclist bikes x distance at 10 miles per hour and returns   [#permalink] 13 Aug 2017, 12:56
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