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Tom drives from town A to town B, driving at a constant speed of 60 mi

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Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 13 Sep 2015, 14:24
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Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?


A. 12
B. 20
C. 24
D. 30
E. 36
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Re: Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 13 Sep 2015, 23:47
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sharmasneha wrote:
Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?


A. 12
B. 20
C. 24
D. 30
E. 36


For average speed, one formula will never fail you:

Average Speed = Total distance/Total Time

Say speed when going from B to C is s. Say distance from B to C is d. So distance from A to B is 2d.

\(36 = \frac{2d + d}{\frac{2d}{60} + \frac{d}{s}}\)
d's get cancelled and you get s = 20.

With practice, you will realise that you don't need to take the variable d since it will anyway get cancelled.

Answer (B)
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Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 13 Sep 2015, 14:40
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Let's assume that it takes 4 hours to go from point A to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to 120/6=20

Hence the answer is B.
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Re: Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 05 Oct 2015, 03:47
d - distance BC
x - speed in BC

2d/60+d/x=3d/36

2160=108x => x=20m/h

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Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 26 Sep 2016, 18:04
Hey Guys,

I am having a tough time understanding the explanation of this question...can anyone help?

Thanks!

Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?


A. 12
B. 20
C. 24
D. 30
E. 36
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Re: Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 26 Sep 2016, 21:40
dre1091 wrote:
Hey Guys,

I am having a tough time understanding the explanation of this question...can anyone help?

Thanks!

Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?


A. 12
B. 20
C. 24
D. 30
E. 36


Merging topics. Please refer to the discussion above.
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Re: Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 26 Sep 2016, 22:15
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dre1091 wrote:
Hey Guys,

I am having a tough time understanding the explanation of this question...can anyone help?

Thanks!

Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?



dre1091

Lets assume distance between town B and C = d.
Distance between town A and B = 2d.
Suppose speed from going to town A to B = x.

We need to find x.

time taken for driving from town A to B = \(\frac{(2d)}{60}\) =\(\frac{d}{30}\)
time taken for driving from town A to B = \(\frac{d}{x}\)

Total time take = \(\frac{d}{30}\) + \(\frac{d}{x}\)
= \(\frac{(d * (x+30))}{(30*x)}\)


Average speed = \(\frac{(Total\ distance)}{(Total\ time)}\)

36 = ( d + 2d ) / \(\frac{(d * (x+30))}{(30*x)}\)

36 =\(\frac{(3 * d * 30 * x )}{(d * (x+30))}\)

\(36 (x+30) = 90x\)

\(4(x+30) = 10x\)

\(4x + 120 = 10x\)

x = 20

This helps ?
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Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 12 Aug 2017, 08:10
dre1091 wrote:
Hey Guys,

I am having a tough time understanding the explanation of this question...can anyone help?

Thanks!

Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?


A. 12
B. 20
C. 24
D. 30
E. 36


hi

there is no alternative to understanding the below concept

3d
___________ = 36
2d/60 + d/x

as you see the "d" will get cancelled out, so this understanding is crucial to answering DS questions. For PS questions, however, you can assume small values for distances for your ease of calculations ...

hope this helps
cheers :lol:
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Re: Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 12 Aug 2017, 10:07
gmatcracker2017 could you please explain how d cancels out?
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Re: Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 12 Aug 2017, 11:31
gmathelp101 wrote:
gmatcracker2017 could you please explain how d cancels out?


hi

look, when you take the LCM of 60 and x, you will get something looking as follows ...


2d( x + 30)
__________
60x

now, 3d into (flip the above equation to eliminate the "d")

that's it ....

hope this helps ..
:)
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Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 12 Aug 2017, 11:48
sharmasneha wrote:
Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?


A. 12
B. 20
C. 24
D. 30
E. 36


let 3=total miles
r=speed from B to C
3/(2/60+1/r)=36
r=20 mph
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Re: Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 12 Aug 2017, 20:38
gmatcracker2017 wrote:
gmathelp101 wrote:
gmatcracker2017 could you please explain how d cancels out?


hi

look, when you take the LCM of 60 and x, you will get something looking as follows ...


2d( x + 30)
__________
60x

now, 3d into (flip the above equation to eliminate the "d")

that's it ....

hope this helps ..
:)

Got it - thank you so much! :)

Sent from my SM-G935F using GMAT Club Forum mobile app
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Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 12 Aug 2017, 21:24
average speed formula for 3 equal distances = 3abc/ab+bc+ac where c is the speed for driving from B to C
AB is twice of BC, so AB can be divided in 2 equal parts
then 3(60*60*c)/(60*60+60c+60c) = 36

180c/(60 + 120c) = 36
180c = 36 (60+120c)
108c = 2160
c = 20
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Re: Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 13 Aug 2017, 11:19
gmathelp101 wrote:
gmatcracker2017 wrote:
gmathelp101 wrote:
gmatcracker2017 could you please explain how d cancels out?


hi

look, when you take the LCM of 60 and x, you will get something looking as follows ...


2d( x + 30)
__________
60x

now, 3d into (flip the above equation to eliminate the "d")

that's it ....

hope this helps ..
:)

Got it - thank you so much! :)

Sent from my SM-G935F using GMAT Club Forum mobile app


good to know that my post helped you ....

Also, for questions with the distance same for 2 cases, you can use harmonic mean ....

2xy
___________
x + y

where x, and y are the velocities of the 2 trips ..

hope this also helps ... :lol:
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Re: Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 13 Aug 2017, 12:24
Let us consider the distance between town A and B is 120. Thus distance between town B and C becomes 60.
Since speed from A to B is 60 mph, time taken is \(\frac{120}{60}\) = 2 hrs.
Now total distance is 120+60 = 180 and speed is 36 mph, thus total time taken is \(\frac{180}{36}\) = 5 hrs.
So to cover 60 miles in remaining 3 hours, he must travel at speed of \(\frac{60}{3}\) = 20 mph
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Re: Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 13 Aug 2017, 19:24
Another easy way to look at this question is
Looking at options (knowing average speed is slightly smaller than average(arithmetic mean) of two speeds
Calculating average of 60 and all options
Option A : average of 60 and 12 = 36, can't be our answer (as average speed cant be equal to average of speeds)
Option B : average of 60 and 20 = 40, possible
Option C : average of 60 and 24 = 42, way too bigger
Option D : average of 60 and 30 = 45, way too bigger
Option E : average of 60 and 36 = 46, way too bigger
Thus answer is Option B : 20
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Re: Tom drives from town A to town B, driving at a constant speed of 60 mi  [#permalink]

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New post 25 Oct 2018, 09:25
sharmasneha wrote:
Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?


A. 12
B. 20
C. 24
D. 30
E. 36


We can let the distance between B and C = d, and thus the distance between A and B = 2d. We can let r = Tom's speed driving from B to C, in miles per hour, and create the equation:

(2d + d)/(2d/60 + d/r) = 36

3d/(d/30 + d/r) = 36

3d = 36d/30 + 36d/r

3 = 6/5 + 36/r

Multiplying both sides of the equation by 5r, we have:

15r = 6r + 180

9r = 180

r = 20

Answer: B
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Re: Tom drives from town A to town B, driving at a constant speed of 60 mi   [#permalink] 25 Oct 2018, 09:25
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