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# A motorist averaged 40 miles per hour on his way to work. He averaged

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A motorist averaged 40 miles per hour on his way to work. He averaged  [#permalink]

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05 May 2017, 02:52
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A motorist averaged 40 miles per hour on his way to work. He averaged 70 miles per hour on his way home along the same route. Which of the following is the closest to his average speed for the round trip?

A. 40
B. 51
C. 55
D. 59
E. 59.5

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A motorist averaged 40 miles per hour on his way to work. He averaged  [#permalink]

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Updated on: 05 May 2017, 10:09
Average Speed = Total distance covered/total time taken

Assuming one way distance is 'D', time taken in onward journey = D/40 and time taken in return journey = D/70

Average speed = (D+D)/(D/40 + D/70). Solve - the variable 'D' will be eliminated and answer = 560/11 = 50.9. closest is '51' or option B

Originally posted by amanvermagmat on 05 May 2017, 03:13.
Last edited by amanvermagmat on 05 May 2017, 10:09, edited 1 time in total.
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Re: A motorist averaged 40 miles per hour on his way to work. He averaged  [#permalink]

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05 May 2017, 06:07
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amanvermagmat wrote:
Average Speed = Total distance covered/total time taken

Assuming one way distance is 'D', time taken in onward journey = D/40 and time taken in return journey = D/70

Average speed = (D+D)/(D/40 + D/70). Solve - the variable 'D' will be eliminated and answer = 560/7 = 50.9. closest is '51' or option B

Hello

Are you sure the final fraction is 560/7 and not 560/11?
Because i have a final fraction of 560/11 which gives the ans 50.9

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Re: A motorist averaged 40 miles per hour on his way to work. He averaged  [#permalink]

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05 May 2017, 08:57
Hi, You all canse use values as well and still get the answer

280 = 40 x time
time = 7

280 = 70 x time
time = 4

560 = speed x 11
speed = 560/11 or 50 10/11

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Re: A motorist averaged 40 miles per hour on his way to work. He averaged  [#permalink]

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05 May 2017, 10:10
khushbumodi wrote:
amanvermagmat wrote:
Average Speed = Total distance covered/total time taken

Assuming one way distance is 'D', time taken in onward journey = D/40 and time taken in return journey = D/70

Average speed = (D+D)/(D/40 + D/70). Solve - the variable 'D' will be eliminated and answer = 560/7 = 50.9. closest is '51' or option B

Hello

Are you sure the final fraction is 560/7 and not 560/11?
Because i have a final fraction of 560/11 which gives the ans 50.9

Sent from my SM-N9200 using GMAT Club Forum mobile app

Yes that was a silly mistake which I have now corrected. thanks.
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Re: A motorist averaged 40 miles per hour on his way to work. He averaged  [#permalink]

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05 May 2017, 10:41
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A motorist averaged 40 miles per hour on his way to work. He averaged 70 miles per hour on his way home along the same route. Which of the following is the closest to his average speed for the round trip?

Average Speed = $$\frac{Total Distance}{Total Time taken}$$

Let distance from Home to Work be D. Therefore Total Distance = D+D = 2D

Time taken from Home to Work =$$\frac{Distance}{Speed}$$ = $$\frac{D}{40}$$
Time taken from Work to Home = $$\frac{Distance}{Speed}$$=$$\frac{D}{70}$$

Therefore Total Time taken = $$\frac{D}{40}$$+ $$\frac{D}{70}$$ = $$\frac{11D}{280}$$

Average Speed =$$\frac{2D}{11D/280}$$ =$$\frac{2D * 280}{11D}$$ =$$\frac{560}{11}$$= 50.9

Closest average speed to 50.9 for the round trip is 51.. Thus Answer B....

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Re: A motorist averaged 40 miles per hour on his way to work. He averaged  [#permalink]

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05 May 2017, 11:12
Since the motorist traveled the same distance both ways, we can calculate his average speed by formula
{2*speed(journey to office)*speed(journey back home)}/Sum of speeds
=(2*40*70)/110
=560/11
=51 approximately(Option B)

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Re: A motorist averaged 40 miles per hour on his way to work. He averaged  [#permalink]

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07 May 2017, 05:06
2
Average Speed = 2*S1*S2/(S1+S2)
=2*40*70/(40+70)
=560/11
=50.9 (approx)

Option B
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Re: A motorist averaged 40 miles per hour on his way to work. He averaged  [#permalink]

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12 May 2017, 12:18
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Bunuel wrote:
A motorist averaged 40 miles per hour on his way to work. He averaged 70 miles per hour on his way home along the same route. Which of the following is the closest to his average speed for the round trip?

A. 40
B. 51
C. 55
D. 59
E. 59.5

We can use the following formula:

average rate = (total distance)/(total time)

If we let the distance between work and home = d, since time = distance/rate, his time going to work is d/40 and his time coming home from work is d/70. Thus:

average rate = 2d/(d/40 + d/70)

average rate = 2d/(7d/280 + 4d/280)

average rate = 2d/(11d/280)

average rate = 560d/11d = 560/11 ≈ 51

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Re: A motorist averaged 40 miles per hour on his way to work. He averaged  [#permalink]

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13 May 2017, 18:51
2
Hi All,

The answers to this question are 'spaced out' in such a way that you don't need to do much math at all to get to the correct answer. This prompt is a fairly common 'design' for a Weighted Average question. Here, a motorist travels a certain distance at one speed, then travels back - the SAME distance - at a different speed. We're asked for the AVERAGE SPEED for the entire trip.

One of the key elements to these types of questions is that the answer will be closer to the slower speed than to the faster speed. The exact 'middle' between 40 and 70 is 55, BUT since the motorist spends MORE time driving 40 mph, the average would have to be closer to 40 (while not being 40 exactly). There's only one answer that 'fits'...

As an aside, GMAT question writers tend to be a bit 'savvier' with how they design the answer choices to these types of questions (meaning that it likely won't be quite this 'easy' to answer this type of question on Test Day)

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Re: A motorist averaged 40 miles per hour on his way to work. He averaged  [#permalink]

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14 May 2017, 22:06
Bunuel wrote:
A motorist averaged 40 miles per hour on his way to work. He averaged 70 miles per hour on his way home along the same route. Which of the following is the closest to his average speed for the round trip?

A. 40
B. 51
C. 55
D. 59
E. 59.5

Average of both speeds = 40 + 70 = 55 m/h

As he took more time while traveling at 40 m/h than while he traveling at 70 m/h.

Then average speed must be more inclined towards slower speed (40 m/h), but it can't be exactly 40 m/h.

So answer is 51 m/h (B).
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Re: A motorist averaged 40 miles per hour on his way to work. He averaged  [#permalink]

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19 May 2017, 03:08
A motorist averaged 40 miles per hour on his way to work. He averaged 70 miles per hour on his way home along the same route. Which of the following is the closest to his average speed for the round trip?

A. 40
B. 51
C. 55
D. 59
E. 59.5
AVG SPEED= 2*a*b/(a+b)
where a = avg speed of motorist on his way to work.
b = avg speed of motorist on his way to home.

So answer is 50.9 which is equal to 51 m/h (B).
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Re: A motorist averaged 40 miles per hour on his way to work. He averaged  [#permalink]

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05 Jul 2020, 02:49
If you are given 2 speed and asked to find the average, you can use the below equation.

Equation :$$\frac{2*S1*S2}{S1+S2}$$

Here, 2 speeds are given.
S1 = 40
S2 = 70

Average speed =$$\frac{2*40*70}{40+70}$$ = 50.9

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Re: A motorist averaged 40 miles per hour on his way to work. He averaged  [#permalink]

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07 Jul 2020, 01:59
2
Since the distance is the same 70*x=40*y with x and y as the different times needed.
Thus, x/y=4/7. Thus, the (weighted) average is: 70*(4/(7+4))+40*(7/(7+4)) ) = 50,9 (B)
Re: A motorist averaged 40 miles per hour on his way to work. He averaged   [#permalink] 07 Jul 2020, 01:59