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# A man travels a distance of 20 miles at 60 miles per hour and then re

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Math Expert
Joined: 02 Sep 2009
Posts: 50009
A man travels a distance of 20 miles at 60 miles per hour and then re  [#permalink]

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01 Mar 2018, 00:43
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Difficulty:

15% (low)

Question Stats:

81% (01:18) correct 19% (01:08) wrong based on 72 sessions

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A man travels a distance of 20 miles at 60 miles per hour and then returns over the same route at 40 miles per hour. What is his average rate for the round trip in miles per hour?

(A) 50

(B) 48

(C) 47

(D) 46

(E) 45

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Director
Joined: 31 Oct 2013
Posts: 651
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: A man travels a distance of 20 miles at 60 miles per hour and then re  [#permalink]

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01 Mar 2018, 04:05
Bunuel wrote:
A man travels a distance of 20 miles at 60 miles per hour and then returns over the same route at 40 miles per hour. What is his average rate for the round trip in miles per hour?

(A) 50

(B) 48

(C) 47

(D) 46

(E) 45

Average speed for the round trip : 2.x.y/x+y
=2.40.60/40+60
=2.40.60/10
=48
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Joined: 22 May 2016
Posts: 2038
A man travels a distance of 20 miles at 60 miles per hour and then re  [#permalink]

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01 Mar 2018, 10:08
1
Bunuel wrote:
A man travels a distance of 20 miles at 60 miles per hour and then returns over the same route at 40 miles per hour. What is his average rate for the round trip in miles per hour?

(A) 50

(B) 48

(C) 47

(D) 46

(E) 45

Average speed = $$\frac{TotalDistance}{TotalTime}$$

RT = D
T = D/R

Note: dividing distance in miles by rate in miles per hour yields time in hours.*

Total time = (Leg 1 + Leg 2)

Leg 1 time: $$\frac{D}{r}=\frac{20mi}{60mph}=\frac{20}{60}hrs=\frac{1}{3}$$ hour

Leg 2 time: $$\frac{D}{r}=\frac{20}{40}=\frac{1}{2}$$ hour

Total time: $$\frac{1}{3}hr +\frac{1}{2}hr=\frac{5}{6}$$ hour

Total Distance = (20mi + 20mi) = 40 miles

Ave speed*: $$\frac{40}{(\frac{5}{6})}=40 *\frac{6}{5}=48$$
mph

*It works because miles units cancel.
$$\frac{miles}{(\frac{miles}{hour})}=(miles*\frac{hour}{miles})=hours$$

**With units. If you stay with time in hours, then you don't need units, but that fact may not be obvious. This example is $$\frac{D}{t}=r$$:
$$\frac{40miles}{(\frac{5}{6}hour)}=(40miles * \frac{6}{5hrs})=48\frac{miles}{hour}=48mph$$
$$\frac{miles}{hour}$$ IS mph

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Re: A man travels a distance of 20 miles at 60 miles per hour and then re  [#permalink]

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02 Mar 2018, 10:36
Bunuel wrote:
A man travels a distance of 20 miles at 60 miles per hour and then returns over the same route at 40 miles per hour. What is his average rate for the round trip in miles per hour?

(A) 50

(B) 48

(C) 47

(D) 46

(E) 45

We can use the following formula:

average = (total distance)/(total time)

Average = 40/(20/60 + 20/40)

Average = 40/(1/3 + 1/2)

Average = 40/(2/6 + 3/6)

Average = 40/(5/6) = 240/5 = 48

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Joined: 21 May 2013
Posts: 651
Re: A man travels a distance of 20 miles at 60 miles per hour and then re  [#permalink]

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02 Mar 2018, 10:54
Bunuel wrote:
A man travels a distance of 20 miles at 60 miles per hour and then returns over the same route at 40 miles per hour. What is his average rate for the round trip in miles per hour?

(A) 50

(B) 48

(C) 47

(D) 46

(E) 45

Average Speed= Total distance traveled/total time taken
=40/(1/3+1/2)=40/(5/6)
=48
Manager
Joined: 23 Sep 2016
Posts: 220
Re: A man travels a distance of 20 miles at 60 miles per hour and then re  [#permalink]

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03 Mar 2018, 03:44
Bunuel wrote:
A man travels a distance of 20 miles at 60 miles per hour and then returns over the same route at 40 miles per hour. What is his average rate for the round trip in miles per hour?

(A) 50

(B) 48

(C) 47

(D) 46

(E) 45

IMO B
i will show in table which is attached bellow
Attachments

Screenshot (82).png [ 77.13 KiB | Viewed 870 times ]

Re: A man travels a distance of 20 miles at 60 miles per hour and then re &nbs [#permalink] 03 Mar 2018, 03:44
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