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Manager  Joined: 07 Feb 2010
Posts: 125
Susan drove an average speed of 30 miles per hour for the  [#permalink]

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23 00:00

Difficulty:   5% (low)

Question Stats: 83% (01:14) correct 17% (01:33) wrong based on 1292 sessions

HideShow timer Statistics Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 60 miles/hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip

A. 35
B. 40
C. 45
D. 50
E. 55

Originally posted by anilnandyala on 02 Nov 2010, 06:56.
Last edited by Bunuel on 13 Oct 2013, 03:01, edited 1 time in total.
Moved to PS forum.
Math Expert V
Joined: 02 Sep 2009
Posts: 55804
Re: susan drove an average speed  [#permalink]

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7
8
anilnandyala wrote:
susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 60 miles/hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip

a 35
b 40
c 45
d 50
e 55

$$average \ speed=\frac{total \ distance \ covered}{total \ time}$$;

Total distance covered = 30 + 30 = 60 miles;
Total time = 30/30 + 30/60 = 3/2 hours;

$$average \ speed=\frac{total \ distance \ covered}{total \ time}=\frac{60}{\frac{3}{2}}=40$$.

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Senior Manager  B
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Re: Susan drove an average speed of 30 mph for the first 30 min  [#permalink]

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Your reasoning is correct. Probably the answer is incorrect unless you have not changed either the question or the answer.
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GMAT 1: 530 Q43 V20 GMAT 2: 560 Q42 V25 GMAT 3: 650 Q48 V31 Re: Susan drove an average speed of 30 mph for the first 30 min  [#permalink]

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Avg. speed = total distance / total time

Total distance = 60 miles
Total time = 30 / 30 + 30/60 = 3/2

Avg. speed = 40.

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Re: Susan drove an average speed of 30 mph for the first 30 min  [#permalink]

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jsphcal wrote:
Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip and then at an average speed of 60 miles per hour for the remaining 30 miles of the trip. If she made no stops during the trip, what was Susan's average speed, in miles per hour, for the entire trip?

a. 35
b. 40
c. 45
d. 50
e. 55

The Common Formula is Average speed = Total distance / Total time.
However if the distances traveled with two different speeds are the same (as 30 in this case), we can calculate the average speed as per following rule.
ratio of two distinct speeds = 1:2
Difference of two distinct speeds = 60 - 30 = 30
Now divide this difference by the sum of intergers of ratio (i.e. by 1+2 = 3 in this case ) 30/3 = 10
Average speed will be 10 X 1 part away from the lower speed i.e. 30 + 10 X 1 = 40.

The benefit of this method is once practiced enough you can calculate the average speed mentally or with minimal calculation and thereby can save valuable time on the GMAT

Regards,

Abhijit
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Originally posted by Narenn on 20 Mar 2013, 02:09.
Last edited by Narenn on 20 Mar 2013, 04:56, edited 1 time in total.
Intern  Joined: 01 Feb 2013
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Concentration: Finance, Technology
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Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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2
My approach:

30/30 -> 1h
30/60 -> 0.5h
---------1.5h total and then 60/1.5 -> 40 (1.5 -> 3 -> 4.5 -> 6)
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Posts: 415
Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 60 miles/hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip

What we have here are equal distances for both segments.

First segment: 30 miles/hour and covered 30 miles, therefore it took one hour.
Second segment: 60 miles/hour and covered 30 miles, therefore it took 1/2 hour.

(Total distance / total time)
(60 / [1hr+ 1/2hr])
(60 / 1.5) = 40 miles avg. speed.

A. 35
B. 40
C. 45
D. 50
E. 55

(B)

When don't we simply add the distances/speeds together to get the average?
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Joined: 23 Dec 2014
Posts: 47
Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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Rate x Time = Distance
Going: 30 x 1 = 30
Returning: 30 x .5 = 30

Avg speed = Total distance/Total Time
=(30+30)/ (1+.5)
=40
Intern  Joined: 25 Jan 2016
Posts: 1
Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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Narenn wrote:
jsphcal wrote:
Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip and then at an average speed of 60 miles per hour for the remaining 30 miles of the trip. If she made no stops during the trip, what was Susan's average speed, in miles per hour, for the entire trip?

a. 35
b. 40
c. 45
d. 50
e. 55

The Common Formula is Average speed = Total distance / Total time.
However if the distances traveled with two different speeds are the same (as 30 in this case), we can calculate the average speed as per following rule.
ratio of two distinct speeds = 1:2
Difference of two distinct speeds = 60 - 30 = 30
Now divide this difference by the sum of intergers of ratio (i.e. by 1+2 = 3 in this case ) 30/3 = 10
Average speed will be 10 X 1 part away from the lower speed i.e. 30 + 10 X 1 = 40.

The benefit of this method is once practiced enough you can calculate the average speed mentally or with minimal calculation and thereby can save valuable time on the GMAT

Regards,

Abhijit

Nice method, but why should it be 10 away from the lower speed and not from the higher speed?
Intern  B
Joined: 18 May 2016
Posts: 35
Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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Why can't we get her average speed by weighting her speed by the proportion of the total distance realized at a certain speed?

e.g. why is 30(30/60)+60(30/60)=15+30 incorrect?

Thank you please let me know if i haven't been clear enough
Manager  B
Joined: 06 Dec 2016
Posts: 243
Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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Hi Bunuel,

I don't know if this approach is right. I got the answer though

distance = speed x time
60 = (30 + 60) x time
60 = 90 x time
60/90 = time
2/3 multiplied by 60 = 40

Therefore, the answer is B. Is my approach correct?
Math Expert V
Joined: 02 Sep 2009
Posts: 55804
Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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matthewsmith_89 wrote:
Hi Bunuel,

I don't know if this approach is right. I got the answer though

distance = speed x time
60 = (30 + 60) x time
60 = 90 x time
60/90 = time
2/3 multiplied by 60 = 40

Therefore, the answer is B. Is my approach correct?

No, that;'s not correct.

Distance = Average Speed * Time.

Distance = 60;
Time = 30/30 + 30/60 = 3/2 hours;

60 = Average Speed * 3/2

Average Speed = 40.
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Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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anilnandyala wrote:
Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 60 miles/hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip

A. 35
B. 40
C. 45
D. 50
E. 55

We are given that Susan drove at an average speed of 30 miles per hour for the first 30 miles of a trip and then at an average speed of 60 miles per hour for the remaining 30 miles of the trip. We must determine her average speed overall. The formula for average speed is:

average speed = total distance/total time

For the first half of the trip, we know that Susan’s speed was 30 mph and her distance was 30 miles, so her time was 30/30 = 1 hour.

For the second half of the trip, we know that Susan’s speed was 60 mph and her distance was 30 miles, so her time was 30/60 = 1/2 hour. Therefore her average speed in miles per hour is:

average speed = (30 + 30)/(1 + ½)

average speed = 60/(3/2)

average speed = 40

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Manager  S
Joined: 03 Jan 2016
Posts: 57
Location: India
WE: Engineering (Energy and Utilities)
Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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30 miles/ Hour speed for 30 miles => Time Takem = 1 Hr.
60 miles/Hour Speed for remaining 30 miles => Time taken = 0.5 Hour.

Avg Speed = 60/(1+0.5) = 40 mph.
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GMAT 1: 730 Q51 V36 Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 60 miles/hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip

A. 35
B. 40
C. 45
D. 50
E. 55

Sol: Average Speed = Total Distance/Total time
Total Distance = 30 miles + 30 miles = 60 miles
Total time = Time taken for the 1st 30 miles + time taken for the next 30 miles
= (30miles/30mph) + (30 miles/60 mph)
= (1 + 0.5) hours
= 1.5 hours

Average speed = Total Distance/Total time = 60/1.5 = 40 mph
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Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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anilnandyala wrote:
Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 60 miles/hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip

A. 35
B. 40
C. 45
D. 50
E. 55

Time taken in travelling 1st 30 miles = 30/30 = 1 hr
Time taken in travelling remaining 30 miles = 30/60 = 1/2 hr
Total distance traveled = 30+30 = 60 miles
Total time taken = 1+1/2 = 3/2 hr
Average speed = $$\frac{60}{(3/2)}$$ = 40 miles/hr
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Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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Here is a very easy formula to remember:

Let a be the first speed
Let b be the second speed

Avg Speed = 2ab/a+b

a = 30
b= 60

Avg Speed = 2(30)(60)/30+60 = 3600/90 = 40
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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Hi All,

To figure out Average Speed for an entire trip, we need TOTAL Distance and TOTAL Time:

Total Distance = (Average Speed)(Total Time)

Here, we're given all of the numerical information we need to calculate each part of the journey:

1st part: 30 miles/hour for 30 miles

30 miles = (30mph)(Time)
30/30 = T hours
T = 1 hour

2nd part: 60 miles/hour for 30 miles
30 miles = (60mph)(Time)
30/60 = T hours
T = 1/2 hour

Total Distance = 30 + 30 = 60 miles
Total Time = 1 + 1/2 = 1.5 hours

Using these values, we can plug in and find the Average Speed for the entire trip:

60 miles = (Average Speed)(1.5 hours)
60/1.5 = Average Speed

Average Speed = 40 mph

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GMAT 1: 620 Q48 V29 Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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Bunuel wrote:
anilnandyala wrote:
susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 60 miles/hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip

a 35
b 40
c 45
d 50
e 55

$$average \ speed=\frac{total \ distance \ covered}{total \ time}$$;

Total distance covered = 30 + 30 = 60 miles;
Total time = 30/30 + 30/60 = 3/2 hours;

$$average \ speed=\frac{total \ distance \ covered}{total \ time}=\frac{60}{\frac{3}{2}}=40$$.

but i think av should be closer to the 60
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Joined: 02 Sep 2009
Posts: 55804
Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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robu1 wrote:
Bunuel wrote:
anilnandyala wrote:
susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 60 miles/hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip

a 35
b 40
c 45
d 50
e 55

$$average \ speed=\frac{total \ distance \ covered}{total \ time}$$;

Total distance covered = 30 + 30 = 60 miles;
Total time = 30/30 + 30/60 = 3/2 hours;

$$average \ speed=\frac{total \ distance \ covered}{total \ time}=\frac{60}{\frac{3}{2}}=40$$.

but i think av should be closer to the 60

It's not clear what you are trying to say. The average speed is 40 miles per hour as shown in all solutions above. Do you have any questions?
_________________ Re: Susan drove an average speed of 30 miles per hour for the   [#permalink] 26 Feb 2018, 23:14

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