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Bruce biked 24 miles to his favorite scenic vista and then t
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25 Dec 2019, 00:41
25 Dec 2019, 00:41
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Question Stats:
61% (02:47) correct
38% (02:30) wrong based on 36 sessions
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Bruce biked 24 miles to his favorite scenic vista and then turned around and biked back along the exact same path. His average speed for the entire trip was 18 miles per hour.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Quantity A |
Quantity B |
The maximum average speed of Bruce's second leg if the first leg took between 60 minutes and 80 minutes |
The minimum average speed of Bruce's first leg if the second leg took between 80 and 100 minutes |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Re: Bruce biked 24 miles to his favorite scenic vista and then t
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26 Dec 2019, 10:49
26 Dec 2019, 10:49
Can you please provide an explanation?
Thank you
Thank you
Re: Bruce biked 24 miles to his favorite scenic vista and then t
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26 Dec 2019, 12:01
26 Dec 2019, 12:01
1
Expert Reply
We do have a total distance of 48 miles, back and forth. 18 is the speed
D= RT
48=18T
T=8/3 hours
Now, for Q A you do need to maximize the time, slow in the first stretch and as fast as possible in the second leg which is 80 minutes or 4/3 hours.
8/3-4/3=4/3 hours
24=r*4/3
r=18 which is the speed
EXACTLY the contrary we have to do for Q B. Maximize the fast in the first stretch and slow in the second. To do so consider 80 minutes which is still 4/3
8/3-4/3=4/3
r (the speed) will be the same. 18 miles per hours
C is the answer.
An alternative approach is to look at the two quantities which balance each other: 60---80 and 80----100
Take the overlap which is 80. The legs are equal to 24. Regardless of the speed, the two quantities must be equal.
The second approach is logic and observation based on common sense.
Regards
D= RT
48=18T
T=8/3 hours
Now, for Q A you do need to maximize the time, slow in the first stretch and as fast as possible in the second leg which is 80 minutes or 4/3 hours.
8/3-4/3=4/3 hours
24=r*4/3
r=18 which is the speed
EXACTLY the contrary we have to do for Q B. Maximize the fast in the first stretch and slow in the second. To do so consider 80 minutes which is still 4/3
8/3-4/3=4/3
r (the speed) will be the same. 18 miles per hours
C is the answer.
An alternative approach is to look at the two quantities which balance each other: 60---80 and 80----100
Take the overlap which is 80. The legs are equal to 24. Regardless of the speed, the two quantities must be equal.
The second approach is logic and observation based on common sense.
Regards
