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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # GRE Math Challenge #7-David drove to work at an average  Question banks Downloads My Bookmarks Reviews Important topics
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GRE Math Challenge #7-David drove to work at an average [#permalink]
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Expert's post 00:00

Question Stats: 58% (01:15) correct 41% (01:21) wrong based on 131 sessions
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)$$\frac{256}{5}$$
C)$$\frac{360}{7}$$
D)$$\frac{105}{2}$$
E)$$\frac{160}{3}$$
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #7-David drove to work at an average [#permalink]
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Re: GRE Math Challenge #7-David drove to work at an average [#permalink]
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The total distance going from home to work = total distance going from work to home
In the 1st case David drove @ an average speed of 45 miles per hour so distance $$d = 45 h1$$where $$h1$$is the time taken to complete the distance
In the 2nd case David drove @ an average speed of 60 miles per hour so distance $$d = 60 h2$$where $$h2$$is the time taken to complete the return journey from work to home
Given,
$$h1 + h2 = 2$$
we get,$$h1 = 2 - h2$$
Since distance is equal for going to work from home and coming back to home from work
$$45h1 = 60h2$$
hence, $$45(2 - h2) = 60 h2$$
solve for h2 it should equal$$\frac{90}{105}$$
Solve for D by replacing value of h2 in the eqn $$60* h2$$
$$d =\frac{360}{7}$$
(C)
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Re: GRE Math Challenge #7-David drove to work at an average [#permalink]
Great Job!!!
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Re: GRE Math Challenge #7-David drove to work at an average [#permalink]
C : 360/7
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Re: GRE Math Challenge #7-David drove to work at an average [#permalink]
From home to work: 45 = t1*d
From work to home: 60 = t2*d

The distance d is the same for both trips, and also t1 + t2 = 2

So t1 = d/45 and t2 = d/60.

Substitute away t1 and t2 in the total time equation: d/45 + d/60 = 2.

Now solving for d: (60d + 45d)/2700 = 2 --> 105*d = 5,400 --> d = 360/7.
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Re: GRE Math Challenge #7-David drove to work at an average [#permalink]
speed = distance/ time

We will get 2 equation for 1. To office and 2. Back from office.

Solving for 2 variables from 2 equations gives the answer.
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Re: GRE Math Challenge #7-David drove to work at an average [#permalink]
the equation is x/45 + x/60 = 2 ==> x = 360/7

where X is the distance between home and office. Target Test Prep Representative Joined: 12 Sep 2018
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Re: GRE Math Challenge #7-David drove to work at an average [#permalink]
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Expert's post
soumya1989 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)$$\frac{256}{5}$$
C)$$\frac{360}{7}$$
D)$$\frac{105}{2}$$
E)$$\frac{160}{3}$$

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

d/45 + d/60 = 2

Multiplying by 180, we have:

4d + 3d = 360

7d = 360

d = 360/7

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Re: GRE Math Challenge #7-David drove to work at an average [#permalink]
Expert's post
soumya1989 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)$$\frac{256}{5}$$
C)$$\frac{360}{7}$$
D)$$\frac{105}{2}$$
E)$$\frac{160}{3}$$

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

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com  Re: GRE Math Challenge #7-David drove to work at an average   [#permalink] 23 Apr 2020, 07:42
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