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Al and Barb shared the driving on a certain trip. [#permalink]
Bunuel wrote:
Al and Barb shared the driving on a certain trip. What fraction of the total distance did Al drive?

(1) Al drove for 3/4 as much time as Barb did. We don't know their average speeds. Not sufficient.

(2) Al's average driving speed for the entire trip was 4/5 of Barb's average driving speed for the trip. We don;t know the times. Not sufficient.

(1)+(2) When combined we have all we need:

Barb's time = t hours, Al's time = 3/4*t hours.
Barb's speed = r miles per hour and Al's rate = 4/5*r miles per hour.

Barb's distance = rt and Al's distance = 3/5*rt --> Al's covered (3/5*rt)/(rt+3/5*rt)=3/8 of the total distance. Sufficient.

Answer: C.


Hi Bunuel
Great explanation.
I had a doubt that since we know that time is proportional to distance if the time taken by Al is 3/4 of the time of B, can't we infer from here that the ratio of there distances is 3/4 and Al drove 3/7 of the total distance??????

Thanks in advance
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Re: Al and Barb shared the driving on a certain trip. [#permalink]
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suramya26 wrote:
Bunuel wrote:
Al and Barb shared the driving on a certain trip. What fraction of the total distance did Al drive?

(1) Al drove for 3/4 as much time as Barb did. We don't know their average speeds. Not sufficient.

(2) Al's average driving speed for the entire trip was 4/5 of Barb's average driving speed for the trip. We don;t know the times. Not sufficient.

(1)+(2) When combined we have all we need:

Barb's time = t hours, Al's time = 3/4*t hours.
Barb's speed = r miles per hour and Al's rate = 4/5*r miles per hour.

Barb's distance = rt and Al's distance = 3/5*rt --> Al's covered (3/5*rt)/(rt+3/5*rt)=3/8 of the total distance. Sufficient.

Answer: C.


Hi Bunuel
Great explanation.
I had a doubt that since we know that time is proportional to distance if the time taken by Al is 3/4 of the time of B, can't we infer from here that the ratio of there distances is 3/4 and Al drove 3/7 of the total distance??????

Thanks in advance


No. Say you drive twice as fast as I do. Can we say that you cover twice as much distance as I do? No, because we don't how long each of us drives. If you drive for 1 hour and I drive for 100 hours, what fraction of the total distance drive?
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Re: Al and Barb shared the driving on a certain trip. [#permalink]
Bunuel wrote:
Al and Barb shared the driving on a certain trip. What fraction of the total distance did Al drive?

(1) Al drove for 3/4 as much time as Barb did. We don't know their average speeds. Not sufficient.

(2) Al's average driving speed for the entire trip was 4/5 of Barb's average driving speed for the trip. We don;t know the times. Not sufficient.

(1)+(2) When combined we have all we need:

Barb's time = t hours, Al's time = 3/4*t hours.
Barb's speed = r miles per hour and Al's rate = 4/5*r miles per hour.

Barb's distance = rt and Al's distance = 3/5*rt --> Al's covered (3/5*rt)/(rt+3/5*rt)=3/8 of the total distance. Sufficient.

Answer: C.

——-
Thanks bunuel for this explanation.

Unfortunately, it took me a long time to arrive at this equation. I also took a value for distance and tried to find the ans - I realised later that I couldn’t do that because we’re trying to find the fraction of the distance itself.

Pls correct me if my logic is incorrect

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Re: Al and Barb shared the driving on a certain trip. [#permalink]
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total distance = average speed * total time

(1) We don't know the average speed of Al or Barb -- we only know the times. Al could have drove 1000 miles and Barb could have drove 2 miles and vice versa. Insufficient.

(2) We don't know the time spent driving by Al or Barb. Insufficient.

(1 & 2) Combined we can determine the total distance.

Barb's distance = rt
Al's distance = 3/4t * 4/5r = 3/5rt

Total distance = rt + 3/5rt
Al covered: (3/5rt) / (rt + 3/5rt) = 3/8 of the trip
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Re: Al and Barb shared the driving on a certain trip. [#permalink]
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Re: Al and Barb shared the driving on a certain trip. [#permalink]
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