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# Alex drives to and from work each day along the same route. If he driv

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VP
Status: Preparing for the GMAT
Joined: 02 Nov 2016
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Alex drives to and from work each day along the same route. If he driv [#permalink]

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04 May 2017, 11:18
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Question Stats:

76% (01:17) correct 24% (00:56) wrong based on 55 sessions

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Alex drives to and from work each day along the same route. If he drives at a speed of 80 miles per hour on the way to work and he drives at a speed of 100 miles per hour on the way from work, which of the following most closely approximates his average speed in miles per hour for the round trip?

A. 80.0
B. 88.9
C. 90.0
D. 91.1
E. 100.0
[Reveal] Spoiler: OA

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Re: Alex drives to and from work each day along the same route. If he driv [#permalink]

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04 May 2017, 11:38
avrg speed(if distance constant)= 2ab/(a+b)
=2*80*100/(100+80)=88.9
ans:B
VP
Joined: 22 May 2016
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Alex drives to and from work each day along the same route. If he driv [#permalink]

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05 May 2017, 07:32
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Especially because no distance is given, the classic trap question.

As an alternative to algebraic approach, plugging in might be quicker or easier for some.

If no distance is given, AND we can assume they're equal, put in any "nice" number. I chose large ones because I did not want to work with fractions.

Average speed = total distance divided by total time

1. Calculate time for each leg

Let 800 be distance one way

D/r= t

Leg #1 to work: 800 miles / 80 mph = 10 hrs

Leg #2 from work: 800 miles / 100 mph = 8 hrs

2. Find average

Total distance is 800 + 800 = 1600

Total time is 10 + 8 = 18

Total distance/total time =

1600/18 = 88.888... = approx 89

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Re: Alex drives to and from work each day along the same route. If he driv [#permalink]

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05 May 2017, 20:04
Average speed = total distance/total time
=( d+d)/(D/80+D/100) Time = distance/speed
=2d*80*100/d*(80+100)
=2*80*100/180
=1600/18
=800/9
=88.88
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Re: Alex drives to and from work each day along the same route. If he driv [#permalink]

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12 May 2017, 12:11
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Expert's post
Alex drives to and from work each day along the same route. If he drives at a speed of 80 miles per hour on the way to work and he drives at a speed of 100 miles per hour on the way from work, which of the following most closely approximates his average speed in miles per hour for the round trip?

A. 80.0
B. 88.9
C. 90.0
D. 91.1
E. 100.0

We can use the following formula:

average rate = (total distance)/(total time)

If we let the distance between work and home = d, since time = distance/rate, his time going to work is d/80 and his time coming home from work is d/100. Thus:

average rate = 2d/(d/80 + d/100)

average rate = 2d/(5d/400 + 4d/400)

average rate = 2d/(9d/400)

average rate = 800d/9d = 800/9 ≈ 88.9

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Re: Alex drives to and from work each day along the same route. If he driv [#permalink]

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12 May 2017, 23:32
Average Speed when distance is constant is given by the formula:
Average Speed= $$\frac{2ab}{a+b}$$
= $$\frac{2*100*80}{100+80}$$
= $$\frac{16000}{180}$$= 88.9

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Re: Alex drives to and from work each day along the same route. If he driv   [#permalink] 12 May 2017, 23:32
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