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Adam and Beth each drove from Smallville to Crown City by different ro

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Adam and Beth each drove from Smallville to Crown City by different ro  [#permalink]

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New post 25 Jun 2016, 21:17
1
6
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

83% (01:38) correct 17% (02:28) wrong based on 179 sessions

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Adam and Beth each drove from Smallville to Crown City by different routes. Adam drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than Adam to complete the trip. How many miles per hour was Beth's average speed on this trip?

(A) 24
(B) 30
(C) 48
(D) 54
(E) 75

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Re: Adam and Beth each drove from Smallville to Crown City by different ro  [#permalink]

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New post 25 Jun 2016, 22:21
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Speed = Distance/Time

Distance for Adam = Speed * Time = 40 * 1/2 = 20 miles

Distance for Beth = Distance for Adam+5 = 20+5 = 25 miles
Time taken by Beth = Time taken by Adam + (1/3 hour) = 1/2+1/3 = 5/6
Speed of Beth = D/T = 25/(5/6) = 25*6/5 = 30 miles per hour

Hence, B is the answer.

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Re: Adam and Beth each drove from Smallville to Crown City by different ro  [#permalink]

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New post 14 Jul 2016, 08:38
1
14101992 wrote:
Speed = Distance/Time

Distance for Adam = Speed * Time = 40 * 1/2 = 20 miles

Distance for Beth = Distance for Adam+5 = 20+5 = 25 miles
Time taken by Beth = Time taken by Adam + (1/3 hour) = 1/2+1/3 = 5/6
Speed of Beth = D/T = 25/(5/6) = 25*6/5 = 30 miles per hour

Hence, B is the answer.

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Quote:

Adam takes 30 mins at speed 40 mph
Convert 30 mins to 1/2 hr.

Let say Beth travels at "s" mph and takes 20 mins more = 50 mins
Convert 50 mins to 5/6 hr

Distance = Speed * Time

Given that Beth travels for 5 more miles.

>>> S * (5/6) - 40*(1/2) = 5
>>> S * (5/6) = 25
>>> S = 30

Answer:B
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Re: Adam and Beth each drove from Smallville to Crown City by different ro  [#permalink]

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New post 14 Jan 2018, 12:09
Hi All,

This question can be solved with a mix of arithmetic and TESTing THE ANSWERS.

We're told that Adam drove 40 mph for 30 minutes. That distance = (40 mph)(1/2 hour) = 20 miles. We're then told that Beth's trip was 5 miles LONGER and 20 minutes MORE to complete - so she traveled for 25 miles and drove for 50 minutes. We're asked for Beth's average speed.

Beth drove for ALMOST an hour; if she had driven for an hour, then she would have an average speed of 25 mph. Since she drove that distance in a little LESS than an hour though, she would have driven a little faster than 25 mph.

Let's TEST Answer B: 30 mph

If she drove 30 mph for 50 minutes, then the total distance traveled would have been (30 mph)(5/6 hour) = 150/6 = 25 miles. This is an exact match for what we were told, so this MUST be the answer.

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Re: Adam and Beth each drove from Smallville to Crown City by different ro  [#permalink]

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New post 25 Jun 2018, 11:11
Shrivathsan wrote:
Adam and Beth each drove from Smallville to Crown City by different routes. Adam drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than Adam to complete the trip. How many miles per hour was Beth's average speed on this trip?

(A) 24
(B) 30
(C) 48
(D) 54
(E) 75


Since Adam drove 30 minutes, or 1/2 hour, at an average speed of 40 mph, he drove 1/2 x 40 = 20 miles. Since Beth’s route was 5 miles longer, she drove 25 miles. She also drove 20 minutes longer than Adam, so she drove for 50 minutes, or 5/6 hour. Thus, her average speed was

25/(5/6) = 25 x 6/5 = 30 mph

Answer: B
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Re: Adam and Beth each drove from Smallville to Crown City by different ro &nbs [#permalink] 25 Jun 2018, 11:11
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