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# Rajesh traveled from home to school at 30 miles per hour. Then he retu

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Math Expert
Joined: 02 Sep 2009
Posts: 49320
Rajesh traveled from home to school at 30 miles per hour. Then he retu  [#permalink]

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03 Jul 2018, 00:11
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Difficulty:

25% (medium)

Question Stats:

77% (01:49) correct 23% (01:37) wrong based on 39 sessions

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Rajesh traveled from home to school at 30 miles per hour. Then he returned home at 40 miles per hour, and finally he went back to school at 60 miles per hour, all along the same route. What was his average speed for the entire trip, in miles per hour?

(A) 32
(B) 36
(C) 40
(D) 45
(E) 47

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Re: Rajesh traveled from home to school at 30 miles per hour. Then he retu  [#permalink]

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03 Jul 2018, 01:42
1
Ans: C
lets say the distance between home and school is S which is travelled all the time.
total distance travelled= 3S
total time taken= S/30 +S/40 + S/60

so Avg speed = Total Dis/Total Time
= (3S)/( S/30 +S/40 + S/60)
This gives us 40 miles/hr speed.

Bunuel wrote:
Rajesh traveled from home to school at 30 miles per hour. Then he returned home at 40 miles per hour, and finally he went back to school at 60 miles per hour, all along the same route. What was his average speed for the entire trip, in miles per hour?

(A) 32
(B) 36
(C) 40
(D) 45
(E) 47

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Re: Rajesh traveled from home to school at 30 miles per hour. Then he retu  [#permalink]

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03 Jul 2018, 03:13
Bunuel wrote:
Rajesh traveled from home to school at 30 miles per hour. Then he returned home at 40 miles per hour, and finally he went back to school at 60 miles per hour, all along the same route. What was his average speed for the entire trip, in miles per hour?

(A) 32
(B) 36
(C) 40
(D) 45
(E) 47

t1=d/30
t2=d/40
t3=d/60
av speed = total distance /total time = 3d/(d/30+d/40+d/60)=3d/9d/120=120/3=40
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Joined: 28 Jun 2018
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Rajesh traveled from home to school at 30 miles per hour. Then he retu  [#permalink]

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03 Jul 2018, 03:38
Could someone smart please explain to me why it's not just the average of all 3 if all 3 paths are equal? Why isn't it just 130/3?

I see that the formula makes sense and the result seems correct. It's messing with my brain.

If it would just be 1 way, where one third of the way he goes 30, one 40, and one 60, it would be 130/3.
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Re: Rajesh traveled from home to school at 30 miles per hour. Then he retu  [#permalink]

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03 Jul 2018, 08:57
2
Bunuel wrote:
Rajesh traveled from home to school at 30 miles per hour. Then he returned home at 40 miles per hour, and finally he went back to school at 60 miles per hour, all along the same route. What was his average speed for the entire trip, in miles per hour?

(A) 32
(B) 36
(C) 40
(D) 45
(E) 47

Let the Distance be 120 miles (LCM of 30, 40 & 60)

So, Time required is $$\frac{120}{30} + \frac{120}{40} + \frac{120}{60}$$ = 4 + 3 + 2

Or, Time required is 9 hours

Since Rajesh traversed the distance 3 times, the total distance travelled is 360 miles, hence average speed is 360/9 = 40 miles/hour, Answer must be (C)
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Re: Rajesh traveled from home to school at 30 miles per hour. Then he retu &nbs [#permalink] 03 Jul 2018, 08:57
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# Rajesh traveled from home to school at 30 miles per hour. Then he retu

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