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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Car B begins moving at 2 mph around a circular track with a radius of
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04 May 2021, 22:04
04 May 2021, 22:04
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Question Stats:
71% (02:21) correct
28% (04:09) wrong based on 7 sessions
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Car B begins moving at 2 mph around a circular track with a radius of 10 miles. Ten hours later, Car A leaves from the same point in the opposite direction, traveling at 3 mph. For how many hours will Car B have been traveling when car A has passed and moved 12 miles beyond Car B?
A. \(4\pi – 1.6\)
B. \(4\pi + 8.4\)
C. \(4\pi + 10.4\)
D. \(2\pi – 1.6\)
E. \(2\pi – 0.8\)
A. \(4\pi – 1.6\)
B. \(4\pi + 8.4\)
C. \(4\pi + 10.4\)
D. \(2\pi – 1.6\)
E. \(2\pi – 0.8\)
Re: Car B begins moving at 2 mph around a circular track with a radius of
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05 May 2021, 03:03
05 May 2021, 03:03
solution plz
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: Car B begins moving at 2 mph around a circular track with a radius of
[#permalink]
16 Dec 2021, 09:10
16 Dec 2021, 09:10
1
Expert Reply
First of all, let's determine the distance of the circular track:
Circumference = pi*d = 20*pi
Now, let's represent each car's distance from the starting point (along the track), t hours from when Car A starts:
B(t) = 20 + 2t [Distance traveled after 10 hours, + 2mph)
A(t) = 20*pi - 3t [Starting at starting point (20pi), -3mph)
We need to determine the time it takes for car A to be 12 miles past car B.
B(t) - A(t) = 12
20 + 2t - (20*pi -3t) = 12
t = (-8 + 20pi)/5
t = 4pi - 1.6
Therefore, car A has been traveling (4pi - 1.6) hours before the criterion is satisfied.The question, however, asks how long car B has been traveling.
t + 10 = 4pi - 1.6 + 10
= 4pi + 8.4
Therefore the answer is B: 4pi + 8.4.
Circumference = pi*d = 20*pi
Now, let's represent each car's distance from the starting point (along the track), t hours from when Car A starts:
B(t) = 20 + 2t [Distance traveled after 10 hours, + 2mph)
A(t) = 20*pi - 3t [Starting at starting point (20pi), -3mph)
We need to determine the time it takes for car A to be 12 miles past car B.
B(t) - A(t) = 12
20 + 2t - (20*pi -3t) = 12
t = (-8 + 20pi)/5
t = 4pi - 1.6
Therefore, car A has been traveling (4pi - 1.6) hours before the criterion is satisfied.The question, however, asks how long car B has been traveling.
t + 10 = 4pi - 1.6 + 10
= 4pi + 8.4
Therefore the answer is B: 4pi + 8.4.
