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

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David drove to work at an average (arithmetic mean) speed of 45 miles  [#permalink]

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New post 22 Oct 2018, 01:29
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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

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Re: David drove to work at an average (arithmetic mean) speed of 45 miles  [#permalink]

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New post 22 Oct 2018, 01:46
Bunuel wrote:
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


Note:- Travelling distance(To & Fro journeys) is equal.
Distance travelled from home to work=Distance travelled from work to home.
Given, \(V_{hw}=45mph\), \(V_{wh}=60mph\), and total travel time,T=2 hrs


Average speed(h-w-h)=Total distance/Total Time

Or, Total distance(h-w-h)=\(v_{avg}*T=\frac{2*V_{hw}*V_{wh}}{V_{hw}+V_{wh}}*T\) =\(\frac{2*45*60*2}{45+60}\)=\(\frac{720}{7}\)
Or, 2*distance from home to work=\(\frac{720}{7}\)
Or, distance from home to work=\(\frac{360}{7}\)

Ans. (C)
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David drove to work at an average (arithmetic mean) speed of 45 miles  [#permalink]

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New post 22 Oct 2018, 02:11
Bunuel wrote:
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


Formula used: Average speed = \(\frac{2*a*b}{a + b}\) where a,b are the average speeds of the to and fro trips

Since David travels one half of the distance at 45 miles per hour and the other half at 60 miles per hour, substituting
the values in the formula, we can calculate the average speed for the entire trip = \(\frac{2*45*60}{105} = \frac{360}{7}\)

David travels a total of 2 hours commuting to and from work.

The total distance that David travels is \(\frac{2*360}{7} = \frac{720}{7}\) (Distance = Speed*Time)

Therefore, David travels one half of that distance to work, which is \(\frac{1}{2}*\frac{720}{7} = \frac{360}{7}\)miles. (Option C)
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Re: David drove to work at an average (arithmetic mean) speed of 45 miles  [#permalink]

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New post 22 Oct 2018, 02:13
45t = 60(2-t)
t = 120/105 = 8/7
d = 45 * 8/7 = 360/7
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Re: David drove to work at an average (arithmetic mean) speed of 45 miles  [#permalink]

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New post 22 Oct 2018, 04:21
David travelled from home to work at an speed= 45 mph
David travelled from work to home at an speed= 60 mph
Total time taken for the trip to and fro = 2 hours

Let the time taken from home to work be "t" hrs.
Then time taken from work to home will be "2-t" hrs.
As the distance on both side are equal:
45t=60(2-t)
45t=120-60t
t= 120/105 hrs

Distance= speed*time= 45*120/105= 360/7 miles.

Ans(C)
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Re: David drove to work at an average (arithmetic mean) speed of 45 miles  [#permalink]

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New post 23 Oct 2018, 07:17
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Time = Distance / Speed
Assuming distance be x
x/45 + x/60 = 2 hours
7x/180 = 2
x = 360/7
C is the answer

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Re: David drove to work at an average (arithmetic mean) speed of 45 miles  [#permalink]

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New post 25 Oct 2018, 09:21
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Bunuel wrote:
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


We can let the distance each way = d and create the equation for time:

d/45 + d/60 = 2

Multiplying by 180, we have:

4d + 3d = 360

7d = 360

d = 360/7

Answer: C
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Re: David drove to work at an average (arithmetic mean) speed of 45 miles  [#permalink]

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New post 12 Jun 2019, 05:47
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Bunuel wrote:
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


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   [#permalink] 12 Jun 2019, 05:47
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