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Rates and Work problem

by gmattesttaker2 » Sun Jul 29, 2012 12:19 pm
Hello,

Can you please assist here:

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
2) Al's average driving speed for the entire trip was 4/5 of Barb's average driving speed for the trip.

Ans: C

Thanks for your help.

Best Regards,
Sri
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Source: — Data Sufficiency |
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by eagleeye » Sun Jul 29, 2012 12:48 pm
gmattesttaker2 wrote:Hello,

Can you please assist here:

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
2) Al's average driving speed for the entire trip was 4/5 of Barb's average driving speed for the trip.

Ans: C

Thanks for your help.

Best Regards,
Sri
In this question we need to find out what is the ratio of distance covered by Al to total distance driven. We can do this if we can find the ratio of distances driven by Al and Barb. With that in mind, let's check the options:

1) Al drove for 3/4 as much time as Barb did
This one talks about the time and not the distance. Distance can change, depending on average speed. Not sufficient.

2) Al's average driving speed for the entire trip was 4/5 of Barb's average driving speed for the trip.
This one talks about the average speed but not the distance. Distance can change depending on time of driving. Insufficient.

Together.

Let the time taken by Barb be T and average speed of Barb be B.
Then Distance traveled by Barb = Time*Speed = T*B --------------------------------(1)
Then Distance traveled by Al = Time*Speed = 3/4T*4/5B = something*(T*B) ----------(2)

Clearly, we can divide the two and find the ratio of the distances traveled, which is what we set out to find. Sufficient. (We don't actually have to find the ratio, we just need to observe that T*B in (1) will cancel with T*B in (2) giving us a number for the ratio)

Hence C is correct.
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by GMATGuruNY » Sun Jul 29, 2012 4:46 pm
gmattesttaker2 wrote:Hello,

Can you please assist here:

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
2) Al's average driving speed for the entire trip was 4/5 of Barb's average driving speed for the trip.

Ans: C

Thanks for your help.

Best Regards,
Sri
To determine whether the two statements combined are sufficient, plug in two different cases that satisfy both statements.

Case 1:
Let Barb's rate = 5 miles per hour and Al's rate = 4 miles per hour.
Let Barb's time = 4 hours and Al's time = 3 hours.
Barb's distance = r*t = 5*4 = 20 miles.
Al's distance = r*t = 4*3 = 12 miles.
Al's distance/total distance = 12/(20+12) = 12/32 = 3/8.

Case 2:
Let Barb's rate = 50 miles per hour and Al's rate = 40 miles per hour.
Let Barb's time = 8 hours and Al's time = 6 hours.
Barb's distance = r*t = 50*8 = 400 miles.
Al's distance = r*t = 40*6 = 240 miles.
Al's distance/total distance = 240/(400+240) = 240/640 = 3/8.

Since in each case Al's distance/total distance = 3/8, the two statements combined are SUFFICIENT.

The correct answer is C.
Last edited by GMATGuruNY on Mon Jul 30, 2012 4:07 am, edited 1 time in total.
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by gmattesttaker2 » Sun Jul 29, 2012 9:18 pm
eagleeye wrote:
gmattesttaker2 wrote:Hello,

Can you please assist here:

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
2) Al's average driving speed for the entire trip was 4/5 of Barb's average driving speed for the trip.

Ans: C

Thanks for your help.

Best Regards,
Sri
In this question we need to find out what is the ratio of distance covered by Al to total distance driven. We can do this if we can find the ratio of distances driven by Al and Barb. With that in mind, let's check the options:

1) Al drove for 3/4 as much time as Barb did
This one talks about the time and not the distance. Distance can change, depending on average speed. Not sufficient.

2) Al's average driving speed for the entire trip was 4/5 of Barb's average driving speed for the trip.
This one talks about the average speed but not the distance. Distance can change depending on time of driving. Insufficient.

Together.

Let the time taken by Barb be T and average speed of Barb be B.
Then Distance traveled by Barb = Time*Speed = T*B --------------------------------(1)
Then Distance traveled by Al = Time*Speed = 3/4T*4/5B = something*(T*B) ----------(2)

Clearly, we can divide the two and find the ratio of the distances traveled, which is what we set out to find. Sufficient. (We don't actually have to find the ratio, we just need to observe that T*B in (1) will cancel with T*B in (2) giving us a number for the ratio)

Hence C is correct.

Hello Eagleeye,

Thanks a lot for the explanation.

Best Regards,
Sri
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by gmattesttaker2 » Sun Jul 29, 2012 9:20 pm
GMATGuruNY wrote:
gmattesttaker2 wrote:Hello,

Can you please assist here:

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
2) Al's average driving speed for the entire trip was 4/5 of Barb's average driving speed for the trip.

Ans: C

Thanks for your help.

Best Regards,
Sri
To determine whether the two statements combined are sufficient, plug in two different cases that satisfy both statements.

Case 1:
Let Barb's rate = 5 miles per hour and Al's rate = 4 miles per hour
Let Barb's time = 4 hours and Al's time = 3 hours.
Barb's distance = r*t = 5*4 = 20 miles.
Al's distance = r*t = 4*3 = 12 miles.
Al's distance/total distance = 12/(20+12) = 12/32 = 3/8.

Case 2:
Let Barb's rate = 50 miles per hour and Al's rate = 40 miles per hour
Let Barb's time = 8 hours and Al's time = 6 hours.
Barb's distance = r*t = 50*8 = 400 miles.
Al's distance = r*t = 40*6 = 240 miles.
Al's distance/total distance = 240/(400+240) = 240/640 = 3/8.

Since in each case Al's distance/total distance = 3/8, the two statements combined are SUFFICIENT.

The correct answer is C.
Hi Mitch,

Thanks a lot for the explanation.

Best Regards,
Sri
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