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

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Bunuel
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Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If [#permalink] New post   23 Feb 2016, 03:00
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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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C
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chetan2u
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Re: Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If [#permalink] New post   23 Feb 2016, 09:47
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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] 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] 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] 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] New post   23 Feb 2016, 16:54
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Re: Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If [#permalink] New post   09 Dec 2019, 10:50
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.


Trip 1 speed = 40 Time =2 Distance =2*40 =80

Total trip = Speed = 30 Time = 2+3 = 5 Distance = 5*30 =150

Trip 2 Distance = Total- Trip 1
= 150 -80 =70

Trip2 Speeed = D/T = 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] New post   05 Feb 2020, 20:38
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.


So 2 hours at 40mph gives us 80miles.

Now total distance = 5 hours * 30 mph = 150 miles

So he covered 70 miles in 3 hours. Speed during that duartion = 70/3mph

Option C.
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Re: Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If [#permalink] New post   21 Apr 2020, 14:04
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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.


We can let r = the average speed of the last three hours of the ride and create the equation:

(40 * 2 + 3r) / 5 = 30

80 + 3r = 150

3r = 70

r = 70/3 mph

Answer: C
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Re: Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If [#permalink] New post   08 Feb 2024, 08:26
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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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