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David drove to work at an average (arithmetic mean) speed of 45 miles per hour.

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by BTGModeratorVI » Wed Apr 22, 2020 11:09 am

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Answers

A

B

C

D

E

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Difficulty—

David drove to work at an average (arithmetic mean) speed of 45 miles per hour. After work, David drove home at an average speed of 60 miles per hour. If David spent a total of 2 hours commuting to and from work, how many miles does David drive to work?

A. 48
B. 256/5
C. 360/7
D. 105/2
E. 160/3

Answer: C
Source: Magoosh
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Re: David drove to work at an average (arithmetic mean) speed of 45 miles per hour.

by Jay@ManhattanReview » Thu Apr 23, 2020 12:44 am
BTGModeratorVI wrote: ↑
Wed Apr 22, 2020 11:09 am
 David drove to work at an average (arithmetic mean) speed of 45 miles per hour. After work, David drove home at an average speed of 60 miles per hour. If David spent a total of 2 hours commuting to and from work, how many miles does David drive to work?

A. 48
B. 256/5
C. 360/7
D. 105/2
E. 160/3

Answer: C
Source: Magoosh
Say the distance is D miles.

Thus, time taken to drive to work = D/45 hours; and time taken to drive to home = D/60 hours

Total time = D/45 + D/60 = 2

=> D = 360/7 miles

The correct answer: C

Hope this helps!

-Jay
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Re: David drove to work at an average (arithmetic mean) speed of 45 miles per hour.

by Brent@GMATPrepNow » Thu Apr 23, 2020 7:42 am
BTGModeratorVI wrote: ↑
Wed Apr 22, 2020 11:09 am
 David drove to work at an average (arithmetic mean) speed of 45 miles per hour. After work, David drove home at an average speed of 60 miles per hour. If David spent a total of 2 hours commuting to and from work, how many miles does David drive to work?

A. 48
B. 256/5
C. 360/7
D. 105/2
E. 160/3

Answer: C
Source: Magoosh
Let's start with a "word equation"
We can write: (David's travel time TO work) + (David's travel time FROM work) = 2 hours
time = distance/speed

Let d = the distance each way

We can write: d/45 + d/60 = 2
To eliminate the fractions, multiply both sides by 180, the LCM of 45 and 60

We get: 4d + 3d = 360
Simplify: 7d = 360
Solve: d = 360/7

Answer: C

Cheers,
Brent
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Re: David drove to work at an average (arithmetic mean) speed of 45 miles per hour.

by Scott@TargetTestPrep » Fri Apr 24, 2020 8:10 am
BTGModeratorVI wrote: ↑
Wed Apr 22, 2020 11:09 am
 David drove to work at an average (arithmetic mean) speed of 45 miles per hour. After work, David drove home at an average speed of 60 miles per hour. If David spent a total of 2 hours commuting to and from work, how many miles does David drive to work?

A. 48
B. 256/5
C. 360/7
D. 105/2
E. 160/3

Answer: C
Source: Magoosh

Solution:

We can create the equation:

d/45 + d/60 = 2

Multiplying by 180, we have:

4d + 3d = 360

7d = 360

d = 360/7

Alternate Solution:

Let t be the time (in hours) that it takes for David to drive to work. Then, it takes 2 - t hours for him to drive home, and we have:

45t = 60(2 - t)

45t = 120 - 60t

105t = 120

t = 120/105 = 8/7

Thus, David drives 45*8/7 = 360/7 miles to work.

Answer: C

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