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

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

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

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New post 01 Mar 2018, 03:05
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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A man travels a distance of 20 miles at 60 miles per hour and then re  [#permalink]

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New post 01 Mar 2018, 09:08
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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

Answer B

*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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New post 02 Mar 2018, 09:36
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

Answer: B
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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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New post 02 Mar 2018, 09:54
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
Answer B
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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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New post 03 Mar 2018, 02:44
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
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Screenshot (82).png
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Re: A man travels a distance of 20 miles at 60 miles per hour and then re &nbs [#permalink] 03 Mar 2018, 02:44
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