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Guy drives 60 miles to attend a meeting. Halfway through, he increases

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Guy drives 60 miles to attend a meeting. Halfway through, he increases  [#permalink]

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New post 08 Nov 2016, 23:03
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Question Stats:

70% (03:14) correct 30% (03:04) wrong based on 218 sessions

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Guy drives 60 miles to attend a meeting. Halfway through, he increases his speed so that his average speed on the second half is 16 miles per hour faster than the average speed on the first half. His average speed for the entire trip is 30 miles per hour. Guy drives on average how many miles per hour during the first half of the way?

A. 12
B. 14
C. 16
D. 24
E. 40

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Re: Guy drives 60 miles to attend a meeting. Halfway through, he increases  [#permalink]

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New post 16 Nov 2016, 09:40
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Bunuel wrote:
Guy drives 60 miles to attend a meeting. Halfway through, he increases his speed so that his average speed on the second half is 16 miles per hour faster than the average speed on the first half. His average speed for the entire trip is 30 miles per hour. Guy drives on average how many miles per hour during the first half of the way?

A. 12
B. 14
C. 16
D. 24
E. 40


Another Method:

Looking at this question, I am immediately reminded of the formula:

AvgSpeed = 2ab/(a+b)

30 = 2*a*(a+16)/(a + a + 16)
15*(2a + 16) = a^2 + 16a
a^2 -14a - 240 = 0
(a - 24)(a + 10) = 0
a = 24

Answer (D)

For more on this:
https://www.veritasprep.com/blog/2015/0 ... -the-gmat/
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Re: Guy drives 60 miles to attend a meeting. Halfway through, he increases  [#permalink]

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New post 08 Nov 2016, 23:38
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1
Bunuel wrote:
Guy drives 60 miles to attend a meeting. Halfway through, he increases his speed so that his average speed on the second half is 16 miles per hour faster than the average speed on the first half. His average speed for the entire trip is 30 miles per hour. Guy drives on average how many miles per hour during the first half of the way?

A. 12
B. 14
C. 16
D. 24
E. 40



IMO D
Let x be the average speed for 1st half of the distance. Then the average speed for 2nd half of the distance will be x+16
avg speed= total distance/total time
30 = 60/{(30/x) + (30/(x+16))}
Solving we get
x^2-14x-240=0
x= -10 or 24
x cant be negative hence x= 24
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Re: Guy drives 60 miles to attend a meeting. Halfway through, he increases  [#permalink]

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New post 09 Nov 2016, 04:17
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Bunuel wrote:
Guy drives 60 miles to attend a meeting. Halfway through, he increases his speed so that his average speed on the second half is 16 miles per hour faster than the average speed on the first half. His average speed for the entire trip is 30 miles per hour. Guy drives on average how many miles per hour during the first half of the way?

A. 12
B. 14
C. 16
D. 24
E. 40


Initial speed = s
After 30 miles, Speed = s+16

Average Speed = Total Distance / Total Time = 60 / [(30/s)+(30/s+16)] = 30 (Given)

Best thing to do here is use options...

A. 12 @s=12, 60 / [(30/s)+(30/s+16)] = 60 / [(30/12)+(30/12+16)] which is not equal to 30 hence INCORRECT
B. 14 @s=12, 60 / [(30/s)+(30/s+16)] = 60 / [(30/14)+(30/14+16)] which is not equal to 30 hence INCORRECT
C. 16 @s=12, 60 / [(30/s)+(30/s+16)] = 60 / [(30/16)+(30/16+16)] which is not equal to 30 hence INCORRECT
D. 24 @s=12, 60 / [(30/24)+(30/24+16)] = 60 / [1.25+0.75] which is equal to 30 hence CORRECT
E. 40
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Re: Guy drives 60 miles to attend a meeting. Halfway through, he increases  [#permalink]

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New post 16 Nov 2016, 09:55
Bunuel wrote:
Guy drives 60 miles to attend a meeting. Halfway through, he increases his speed so that his average speed on the second half is 16 miles per hour faster than the average speed on the first half. His average speed for the entire trip is 30 miles per hour. Guy drives on average how many miles per hour during the first half of the way?

A. 12
B. 14
C. 16
D. 24
E. 40


I assigned values for first segment speed = x. time for first segment 30/x
second part of the trip, speed = x+16. time for second segment 30/x+16

we are told the average speed, we know the total time, and we know the total distance. we can find X.

total time: 30/x + 30/x+16 = (60x+480)/x(x+16)
now..rate is 30, and total distance is 60
30*(60x+480)/x(x+16) = 60
or
(60x+480)/x(x+16) = 2
60x+480 = 2x^2 + 32x
2x^2 - 28x - 480 = 0 | divide by 2
x^2 - 14x - 240 = 0
(x-24)(x+10)=0
x=24 or x=-10
since speed can't be negative, x must be 24.
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Re: Guy drives 60 miles to attend a meeting. Halfway through, he increases  [#permalink]

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New post 24 May 2017, 21:58
Bunuel wrote:
Guy drives 60 miles to attend a meeting. Halfway through, he increases his speed so that his average speed on the second half is 16 miles per hour faster than the average speed on the first half. His average speed for the entire trip is 30 miles per hour. Guy drives on average how many miles per hour during the first half of the way?

A. 12
B. 14
C. 16
D. 24
E. 40


Since overall average speed is 30.

\(30 = \frac{2*x*(x+16)}{2x+16}\)

testing options..
D
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Re: Guy drives 60 miles to attend a meeting. Halfway through, he increases  [#permalink]

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New post 31 May 2017, 18:00
Bunuel wrote:
Guy drives 60 miles to attend a meeting. Halfway through, he increases his speed so that his average speed on the second half is 16 miles per hour faster than the average speed on the first half. His average speed for the entire trip is 30 miles per hour. Guy drives on average how many miles per hour during the first half of the way?

A. 12
B. 14
C. 16
D. 24
E. 40


We can let the rate for the first half of the trip = r and the rate for the second half = r + 16. We also know that the distance for the first half = 30 and for the second half = 30. Thus, the time for the first half is 30/r and the time for the second half is 30/(r + 16).

Let’s now determine r:

average = (total distance)/(total time)

30 = 60/(30/r + 30/(r + 16))

Let’s solve r by dividing the numerator and denominator by 30:

30 = 2/[(1/r) + 1/(r + 16)]

30[(1/r) + 1/(r + 16] = 2

15(1/r + 1/(r + 16) = 1

15/r + 15/(r + 16) = 1

Let’s multiply both sides by r(r + 16):

15(r + 16) + 15r = r(r + 16)

15r + 240 + 15r = r^2 + 16r

r^2 - 14r - 240 = 0

(r + 10)(r - 24) = 0

r = -10 or r = 24

Since r can’t be negative, r = 24.

Answer: D
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Re: Guy drives 60 miles to attend a meeting. Halfway through, he increases  [#permalink]

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