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Intern  Joined: 22 Mar 2010
Posts: 38
A car travels from Mayville to Rome at an average speed of 3  [#permalink]

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14 00:00

Difficulty:   25% (medium)

Question Stats: 76% (01:37) correct 24% (01:35) wrong based on 491 sessions

### HideShow timer Statistics A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?

○ 32.0
○ 33.0
○ 34.3
○ 35.5
○ 36.5

Originally posted by EnterMatrix on 18 Jul 2010, 10:53.
Last edited by Bunuel on 27 Jun 2013, 01:26, edited 1 time in total.
Edited the OA.
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EnterMatrix wrote:
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?
○ 32.0
○ 33.0
○ 34.3
○ 35.5
○ 36.5

Choose some smart number for the distance from Mayville to Rome: let the distance be 120 miles (120 is LCM of 30 and 40 and this will make further calculations easier).

$$Average \ speed=\frac{total \ distance}{total \ time}$$ --> so the nominator, total distance would be $$2*120=240$$;

Total time equals time from Mayville to Rome plus time from Rome to Mayville --> $$\frac{120}{30}+\frac{120}{40}=7$$;

$$Average \ speed=\frac{total \ distance}{total \ time}=\frac{240}{7}\approx{34.3}$$.

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IMO C

EnterMatrix wrote:
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?
○ 32.0
○ 33.0
○ 34.3
○ 35.5
○ 36.5

Solution:

Average speed for the entire trip = 2uv/(u+v),
where u = speed of going
v = speed of returning

Thus, average speed = 2*40*30/(70) = 34.3 mi/h

Hence, C
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EnterMatrix wrote:
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?
○ 32.0
○ 33.0
○ 34.3
○ 35.5
○ 36.5

It is pretty involuntary to come up with 35 miles per hour as the average speed in this case. But, that is wrong. Since, the car has taken more time to travel at 30 mph and less time to travel at 40 mph, the avg speed of the car would be somewhere between 30 and 35(mean) and closer to 35. If I had no time on my hands and had to make a calculated guess, I would have chosen C.

The correct way to find the avg speed is to calculate the total distance and the total time and divide the total distance by total time.

Let the one way distance in this case be D. So the total distance is 2D(travelled over the same route twice)

Total Time = Time taken to travel distance D at 30 mph + time taken to travel distance D at 40 mph
= $$(D/30) + (D/40)$$
= $$7D/120$$
Thus avg speed = Total distance/total time
= $$(2D)/(7D/120)$$
= 34.285

Hope it helps,
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A car travels from Mayville to Rome at an average speed of 3  [#permalink]

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We can pick any number for distance that is divisible by both 30 and 40. Since we have rate and distance, by plugging in the rate formula (r=d/t) we can solve for the average rate/speed
City` Rate--- Time ---Distance
M-R.... 30--- 4 ---- 120
R-M ... 40 --- 3 ---- 120
Total 34.28 --- 7 ---- 240
34.28 ~ 34.3
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Re: A car travels from Mayville to Rome at an average speed of 3  [#permalink]

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EnterMatrix wrote:
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?

○ 32.0
○ 33.0
○ 34.3
○ 35.5
○ 36.5

This is just an approximation and round trip problem- we simply pick a value- which is usually the LCM

Total Distance= Avgspeed * Total Time

120/30= 4
120/40= 3

240= average speed * 7

240/7= 34.3
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Re: A car travels from Mayville to Rome at an average speed of 3  [#permalink]

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Top Contributor
EnterMatrix wrote:
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?

A) 32.0
B) 33.0
C) 34.3
D) 35.5
E) 36.5

We can solve this one quickly if we assign a "nice" distance between Mayville and Rome ("nice" means a distance that works well with 30 miles per hour AND 40 miles per hour)

So, let's say the distance between Mayville and Rome = 120 miles

Time = distance/speed
So, time from Mayville and Rome (at 30 mph) = 120/30 = 4 hours
Time from Rome to Mayville (at 40 mph) = 120/40 = 3 hours

Average speed = (total distance traveled)/(total time)
= (120 + 120)/(4 + 3)
= 240/7
= 34.something (if we use long division here, we'll stop once we get to the ones digit)

Cheers.
Brent
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Re: A car travels from Mayville to Rome at an average speed of 3  [#permalink]

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EnterMatrix wrote:
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?

○ 32.0
○ 33.0
○ 34.3
○ 35.5
○ 36.5

We can use the average rate formula: average = total distance/total time, and let the distance each way = 120 miles. (Note that we could use any number for the distance, but we have chosen the convenient number 120 because it is evenly divisible by both 30 and 40, making the arithmetic easier.)
average = 240/(120/30 + 120/40)

average = 240/(4 + 3) = 240/7 = 34.3

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Re: A car travels from Mayville to Rome at an average speed of 3  [#permalink]

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EnterMatrix wrote:
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?

○ 32.0
○ 33.0
○ 34.3
○ 35.5
○ 36.5

Total distance = D + D = 2D

Total time = D/30 +D/40

Avg. Speed = Total distance / Total time

Avg. Speed =$$\frac{(2D)}{(D/30 + D/40)}$$

Avg. Speed = $$\frac{240D}{70D}$$

Avg. Speed = 34.2 approx

Hence (C)
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Re: A car travels from Mayville to Rome at an average speed of 3  [#permalink]

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For Avg speed if two speeds are given formula is Avg speed=2*S1*S2/S1+S2=34.2
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Re: A car travels from Mayville to Rome at an average speed of 3  [#permalink]

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AkshdeepS wrote:
EnterMatrix wrote:
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?

○ 32.0
○ 33.0
○ 34.3
○ 35.5
○ 36.5

Total distance = D + D = 2D

Total time = D/30 +D/40

Avg. Speed = Total distance / Total time

Avg. Speed =$$\frac{(2D)}{(D/30 + D/40)}$$

Avg. Speed = $$\frac{240D}{70D}$$

Avg. Speed = 34.2 approx

Hence (C)

can you please explain how you reached to Avg. Speed = $$\frac{240D}{70D}$$ ?
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Re: A car travels from Mayville to Rome at an average speed of 3  [#permalink]

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If the distance is equal in both trips, then
Average speed =2xy/(x+y)
=2*30*40/70
=34.3 miles/hr
x=speed in first trip
y= speed in second trip Re: A car travels from Mayville to Rome at an average speed of 3   [#permalink] 21 Apr 2019, 20:06
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