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A car traveled 65% of the way from Town A to Town B at an average spee

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A car traveled 65% of the way from Town A to Town B at an average spee  [#permalink]

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New post Updated on: 24 May 2016, 01:27
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A car traveled 65% of the way from Town A to Town B at an average speed of 65 mph.
The car traveled at an average speed of v mph for the remaining part of the trip.
The average speed for the entire trip was 50 mph. What is v in mph?

(A) 65
(B) 50
(C) 45
(D) 40
(E) 35

Source: Nova's GMAT Math Prep

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Originally posted by DensetsuNo on 24 May 2016, 01:18.
Last edited by DensetsuNo on 24 May 2016, 01:27, edited 2 times in total.
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A car traveled 65% of the way from Town A to Town B at an average spee  [#permalink]

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New post Updated on: 24 May 2016, 06:25
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My take:
\(Distance = Rate\) x \(Time\)

We will solve this problem as \(\frac{D1}{R1} + \frac{D2}{R2} = \frac{Dtot}{Rtot}\)

Whenever we have a % as a distance, that percentage becomes our distance (since the real distance would be a multiple of it)
Therefore \(D1=65\) \(D2=35\) \(Dtot=100\).

As for the rate we knew: \(R1=65mph\) \(R2=v\) \(Rtot=50mph\)

Therefore \(\frac{65}{65} + \frac{35}{v} = \frac{100}{50}\) -> \(1 + \frac{35}{v} = 2\) -> \(v = 35\)

Originally posted by DensetsuNo on 24 May 2016, 01:26.
Last edited by DensetsuNo on 24 May 2016, 06:25, edited 1 time in total.
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Re: A car traveled 65% of the way from Town A to Town B at an average spee  [#permalink]

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New post 24 May 2016, 03:35
DensetsuNo wrote:
A car traveled 65% of the way from Town A to Town B at an average speed of 65 mph.
The car traveled at an average speed of v mph for the remaining part of the trip.
The average speed for the entire trip was 50 mph. What is v in mph?

(A) 65
(B) 50
(C) 45
(D) 40
(E) 35

Source: Nova's GMAT Math Prep

Kudos for nice answers.



Similar question to practice: a-car-traveled-75-of-the-way-from-town-a-to-town-b-at-an-149921.html
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Re: A car traveled 65% of the way from Town A to Town B at an average spee  [#permalink]

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New post 24 May 2016, 04:18
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DensetsuNo wrote:
A car traveled 65% of the way from Town A to Town B at an average speed of 65 mph.
The car traveled at an average speed of v mph for the remaining part of the trip.
The average speed for the entire trip was 50 mph. What is v in mph?

(A) 65
(B) 50
(C) 45
(D) 40
(E) 35

Source: Nova's GMAT Math Prep

Kudos for nice answers.



Assume total distance = 100miles

Time taken for 65 miles = 65/65 = 1 hour
Time taken for the rest of the 35 miles = 35/v hours.

Average speed = 50
Therefore the total time needed = 2 hours.

2 = 1 + 35/v
Hence v = 35 mph

Correct Option: E
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Re: A car traveled 65% of the way from Town A to Town B at an average spee  [#permalink]

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New post 24 May 2016, 05:11
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DensetsuNo wrote:
A car traveled 65% of the way from Town A to Town B at an average speed of 65 mph.
The car traveled at an average speed of v mph for the remaining part of the trip.
The average speed for the entire trip was 50 mph. What is v in mph?

(A) 65
(B) 50
(C) 45
(D) 40
(E) 35

Source: Nova's GMAT Math Prep

Kudos for nice answers.



Let the total distance be x
.65x is travelled with speed 65 mph and .35x is travelled with speed v

Avg speed= total distance/total time
50= x/.65x/65+.35x/v
50= 1/.01+.35/v
50= v/.0v+.35
.5v + 17.5= v
v= 35 mph

E is the answer
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A car traveled 65% of the way from Town A to Town B at an average spee  [#permalink]

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New post 24 May 2016, 06:32
1
DensetsuNo wrote:
A car traveled 65% of the way from Town A to Town B at an average speed of 65 mph.
The car traveled at an average speed of v mph for the remaining part of the trip.
The average speed for the entire trip was 50 mph. What is v in mph?

(A) 65
(B) 50
(C) 45
(D) 40
(E) 35

Source: Nova's GMAT Math Prep

Kudos for nice answers.




Hi,
There can be two three ways..

1) choices-
When the distance covered is same at two different speeds A and B, the average speed is\(\frac{2AB}{A+B}\)...

here let the second speed be x so average =\(\frac{2*x*65}{x+65}= 50\)................\(130x= 50x + 50*65............80x = 50*65 \approx{50*64}...............x = 40\)....
so, if the distance travelled was same, speed would be nearly 40....
But here distance travelled at 65 is 65% of total distance, so speed for lesser distance has to be less than 40..
ONLY 35 is in choice
E

2) let the distance be 100 miles..
65% = 65 miles...
so time taken to travel \(65 miles @ 65mph = \frac{65}{65}= 1\)hr....
Total time takem = \(100 miles @ 50mph = \frac{100}{50} =2\)hr...
so the remaining 35% or 35 miles was travelled in 1 hour, so speed = 35/1 = 35mph
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Re: A car traveled 65% of the way from Town A to Town B at an average spee  [#permalink]

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New post 18 Aug 2018, 09:49
lats say total distance from A to B is 100 miles
65 miles is traveled by 65 miles/hour so it took 1 hour
100 miles is traveled by 50 miles/hour so it took 2 hours

so 35 miles distance is covered in 1 hour
hence v = 35/1 = 35 miles/hour

Answer is E
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Re: A car traveled 65% of the way from Town A to Town B at an average spee  [#permalink]

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New post 20 Aug 2018, 11:32
DensetsuNo wrote:
A car traveled 65% of the way from Town A to Town B at an average speed of 65 mph.
The car traveled at an average speed of v mph for the remaining part of the trip.
The average speed for the entire trip was 50 mph. What is v in mph?

(A) 65
(B) 50
(C) 45
(D) 40
(E) 35



We can let the distance from Town A to Town B = 100 miles. So the car traveled the first 65 miles at 65 mph and the last 35 miles at v mph. Since total distance/total time = average rate, we have:

100/(65/65 + 35/v) = 50

100/(1 + 35/v) = 50

100 = 50(1 + 35/v)

2 = 1 + 35/v

1 = 35/v

v = 35

Answer: E
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Re: A car traveled 65% of the way from Town A to Town B at an average spee &nbs [#permalink] 20 Aug 2018, 11:32
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