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Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If

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Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If [#permalink]

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Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride?

A. 14 mph
B. 20 mph
C. 70/3 mph
D. 80/3 mph
E. 34 mph

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[Reveal] Spoiler: OA

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Re: Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If [#permalink]

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Bunuel wrote:
Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride?

A. 14 mph
B. 20 mph
C. 70/3 mph
D. 80/3 mph
E. 34 mph

Kudos for correct solution.


Hi,
there are various ways we could do the Q..

1) weighted average--
40 is higher and let x be the lower speed ... ratio of time for 40:x=2:3
since 30 is the average, 40 -3/5 * (40-x)=30..
so 3*8-3/5 x=10..
3/5 x=14 or x=70/3.. ans C


2) average method--
2 hrs at 40 and 3 hrs at x= 40*2+3x..
average= (80+3x)/5=30..
80+3x=150..
3x=70 or x=70/3..
C

3) POE--
If you do not know the method, you can get you rprob of correct answer to 1/2 from 1/5
since the average is 30, the answer has to be less than 30 so E is out..
If the time was only four hours, two at 40 and two at the lower speed, 30 will be equidistant, so 20 will be the answer but travelling has been more at lower so >20..a and B are out
only two C and D are left

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Re: Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If [#permalink]

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New post 23 Feb 2016, 09:59
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Bunuel wrote:
Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride?

A. 14 mph
B. 20 mph
C. 70/3 mph
D. 80/3 mph
E. 34 mph

Kudos for correct solution.


Average speed for first two hours, S1 = 40 mph
Distance travelled in these two hours, D1 = 80 miles

Average speed for the entire 5 hour ride, S = 30 mph
Total Distance traveller in the entire 5 hour ride, D = 30 x 5 = 150 miles.

Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 150 - 80 = 70
Average speed for the latter 3 hour period S2 = D2/3 = 70/3
Hence, the correct answer is C

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Re: Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If [#permalink]

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New post 23 Feb 2016, 11:17
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let s=average speed over three hour portion of ride
total distance=80+3s miles
total time=5 hours
average speed for entire trip=(80+3s)/5=30 mph
s=70/3 mph

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Re: Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If [#permalink]

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New post 23 Feb 2016, 13:03
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In 2 hrs at 40mph he covered 80m
In 3 hrs at Xmph he covered 3Xm
(80+3X)/5=30
3X= 70
X=70/3
Ans:C

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Re: Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If [#permalink]

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Re: Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If [#permalink]

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Re: Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If   [#permalink] 13 Aug 2017, 13:50
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