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A car traveled 75% of the way from town A to town B by traveling at T

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Madelaine88
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A car traveled 75% of the way from town A to town B by traveling at T [#permalink] New post   27 Feb 2011, 11:53
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A car traveled 75% of the way from town A to town B by traveling at T hours at an average speed of V mph. The car travels at an average speed of S mph for the remaining part of the trip. Which of the following expressions represents the average speed for the entire trip?

A. 0.75V + 0.25S
B. 0.75T + 0.25S
C. VT/(3S)
D. 4VT/(T+S)/3
E. 4VS/(3S+V)
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E
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Re: A car traveled 75% of the way from town A to town B by traveling at T [#permalink] New post   27 Feb 2011, 12:18
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Let distance AB = 100 miles

75 miles @ V mph, time = 75/V
25 miles @ S mph, time = 25/S

Average speed = 100 / [75/V + 25/S] = 4VS/ 3S+V

Madelaine88 wrote:
A car traveled 75% of the way from town A to town B by traveling at T hours at an average speed of V mph. The car travels at an average speed of S mph for the remaining part of the trip. Which of the following expressions represents the average speed for the entire trip?

A/ .75V+.25S
B/ .75T+.25S
C/ VT/3S
D/ 4VT/((T+S)/3)
E/ 4VS/ 3S+V
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Re: A car traveled 75% of the way from town A to town B by traveling at T [#permalink] New post   27 Feb 2011, 12:34
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Let the distance between A and B be x.

T = 3/4* x/V
x = 4VT/3

Remaining distance = 0.25* VT/0.75 = VT/3

v_{avg} = Total Distance/(Time taken to travel 75%+Time taken to travel 25%)

\(v_{avg} = \frac{4VT}{3(T+\frac{VT}{3S})}\)

\(v_{avg} = \frac{4V}{3(1+\frac{V}{3S})}\)

\(v_{avg} = \frac{4VS}{(3S+V)}\)

Ans: "E"
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Re: A car traveled 75% of the way from town A to town B by traveling at T [#permalink] New post   02 Dec 2016, 03:36
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Madelaine88 wrote:
A car traveled 75% of the way from town A to town B by traveling at T hours at an average speed of V mph. The car travels at an average speed of S mph for the remaining part of the trip. Which of the following expressions represents the average speed for the entire trip?

A. 0.75V + 0.25S
B. 0.75T + 0.25S
C. VT/(3S)
D. 4VT/(T+S)/3
E. 4VS/(3S+V)


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Re: A car traveled 75% of the way from town A to town B by traveling at T [#permalink] New post   12 Dec 2018, 14:53
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Bunuel, I need help with this one. Can you please provide more detail to how you solved this problem? Thanks.

[quote="Bunuel"]
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Re: A car traveled 75% of the way from town A to town B by traveling at T [#permalink] New post   21 Apr 2021, 07:01
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Madelaine88 wrote:
A car traveled 75% of the way from town A to town B by traveling at T hours at an average speed of V mph. The car travels at an average speed of S mph for the remaining part of the trip. Which of the following expressions represents the average speed for the entire trip?

A. 0.75V + 0.25S
B. 0.75T + 0.25S
C. VT/(3S)
D. 4VT/(T+S)/3
E. 4VS/(3S+V)

Solution:

The distance traveled at V mph is TV. Since this is 75% of the total distance, the total distance is TV/0.75 = TV/(3/4) = 4VT/3. Furthermore, ¼(4VT/3) = VT/3 miles are traveled at a speed of S mph, so (VT/3)/S = VT/(3S) hours are spent on traveling at S mph. Since average speed = total distance/total time, we have:

Average speed = (4VT/3) / (T + VT/(3S))
Average speed = (4VTS) / (3ST + VT)

Average speed = (4VS) / (3S + V)

Answer: E
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Re: A car traveled 75% of the way from town A to town B by traveling at T [#permalink] New post   05 Apr 2023, 02:45
Hey ScottTargetTestPrep thank you for your explanation! I struggle with this one:
Quote:
Furthermore, ¼(4VT/3) = VT/3 miles are traveled at a speed of S mph, so (VT/3)/S = VT/(3S) hours are spent on traveling at S mph
Why do we calculate 1/4 of (4VT/3). 1/4 of 3/4 is something different isn't it? I totally understand the rest, it would be really helpful if you could explain this one?

Thank you in advance.
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Re: A car traveled 75% of the way from town A to town B by traveling at T [#permalink] New post   14 Apr 2023, 09:36
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nicbo wrote:
Hey ScottTargetTestPrep thank you for your explanation! I struggle with this one:
Quote:
Furthermore, ¼(4VT/3) = VT/3 miles are traveled at a speed of S mph, so (VT/3)/S = VT/(3S) hours are spent on traveling at S mph
Why do we calculate 1/4 of (4VT/3). 1/4 of 3/4 is something different isn't it? I totally understand the rest, it would be really helpful if you could explain this one?

Thank you in advance.


Remember that the total distance is 4VT/3. We know that 75% = 3/4 of this distance was traveled at a rate of V mph, so the remaining part was 1 - 3/4 = 1/4 of the total distance. Since we are told that the remaining distance was traveled at 5 mph, we take 1/4 of 4VT/3.
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Re: A car traveled 75% of the way from town A to town B by traveling at T [#permalink] New post   14 Apr 2023, 10:55
chowarth wrote:
Bunuel, I need help with this one. Can you please provide more detail to how you solved this problem? Thanks.

Bunuel wrote:



looking for easy to understand kind of solution to such problems
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A car traveled 75% of the way from town A to town B by traveling at T [#permalink] New post   20 Apr 2023, 02:21
nicbo wrote:
Hey ScottTargetTestPrep thank you for your explanation! I struggle with this one:
Quote:
Furthermore, ¼(4VT/3) = VT/3 miles are traveled at a speed of S mph, so (VT/3)/S = VT/(3S) hours are spent on traveling at S mph
Why do we calculate 1/4 of (4VT/3). 1/4 of 3/4 is something different isn't it? I totally understand the rest, it would be really helpful if you could explain this one?

Thank you in advance.


Jitesh8 wrote:
chowarth wrote:
Bunuel, I need help with this one. Can you please provide more detail to how you solved this problem? Thanks.

Bunuel wrote:


looking for easy to understand kind of solution to such problems


Hmm, Let me give it a try. :)

\(Average Speed = \frac{Total Distance}{Total Time}\\
Average Speed = \frac{D}{(T₁ + T₂)}\\
Since, T₁ = \frac{0.75D}{V}.\\
and, T₂ = \frac{0.25D}{S}. \)
So substituting these, we get:
\(\\
\frac{D}{[0.75D/V + 0.25D/S]}.\\
= \frac{D}{D[0.75/V + 0.25/S]}.\\
= \frac{VS}{(0.75S + 0.25V)}.\\
= \frac{VS}{[3S/4 + 1V/4] }.\\
= \frac{4VS}{(3S + V). }.\)
So, Answer is E.
I hope this makes sense. :)
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Re: A car traveled 75% of the way from town A to town B by traveling at T [#permalink] New post   16 Jan 2024, 22:35
karishma

I was wondering, if the average speed formula (2ab/a+b) can be applied in situations, where the distance is not equal, IF, we calculate the individual speeds first, for e.g.
75/v and 25/s here?

I know this is not a suitable approach here, as the answers need variables, but I wonder if this approach would work in another question, where we needed the average speed as a value?
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Re: A car traveled 75% of the way from town A to town B by traveling at T [#permalink] New post   16 Jan 2024, 23:25
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TargetMBA007 wrote:
karishma

I was wondering, if the average speed formula (2ab/a+b) can be applied in situations, where the distance is not equal, IF, we calculate the individual speeds first, for e.g.
75/v and 25/s here?

I know this is not a suitable approach here, as the answers need variables, but I wonder if this approach would work in another question, where we needed the average speed as a value?


No, we cannot use 2ab/(a+b) when the distances are not equal. It will get modified as per the fraction of the distance covered at each speed and hence, we should use the basic formula Avg Speed = Total Distance/Total Time. The 2ab/(a+b) is derived from this very basic formula.

Assuming total distance is d, \(AvgSpeed = \frac{d}{\frac{3d/4}{v} + \frac{d/4}{s}} = \frac{4vs}{3s+v}\\
\)
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Re: A car traveled 75% of the way from town A to town B by traveling at T [#permalink]
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