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

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

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New post 03 Jul 2018, 00:11
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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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New post 03 Jul 2018, 01:42
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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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New post 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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Rajesh traveled from home to school at 30 miles per hour. Then he retu  [#permalink]

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New post 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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New post 03 Jul 2018, 08:57
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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  [#permalink]

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New post 20 Oct 2018, 07:26
let the distance each travelled be "x"
so, all 3 travelled distance = 3x

average speed= total distance/total time
s=3x/(x/30+x/40+x/60)
s= 40 mph

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

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New post 19 Nov 2018, 16:07
nigg777 wrote:
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.


nigg777 Lets dissect the fundamental formula first:

Total Distance (d) = Average Speed (s) x Total Time (t) ===>This means it takes a certain time=t to travel a certain distance=d at a speed=s.

Don't continue reading until you get an image of what the equation and its explanation in bold states.

To reaffirm your understanding, ask yourself this question. If it took you 1 hour to go to your school and then 1 hour to come back home, what is the total time you travelled? Your answer should be 2 hours. (Explanation: Total time = Time going to school + time coming back home = 1 hour + 1 hour = 2 hours

You can also apply the same concept above to your understanding with regards to distance. Total distance = Distance going to school + Distance coming back home.

Now try to apply this concept to speeds. You just can't because it just doesn't make sense. (If you drove at 40 mph to school then came back home at 70 mph, does this mean you drove a total of 110mph? The concept of total speeds does not exist so far)

If you're good so far, the table below would fully answer your question.

_____________| Distance | Average Speed| Time[/u]
Home to School|___ d ___|____ 30 _____| d/30
School to Home|___ d ___|____ 40 _____| d/40
Home to School|___ d ___|____ 60 _____| d/60
Total_________|d+d+d=3d|_____ S ____ | d/30+d/40+d/60 (We added total distance travelled and we added total time taken to travel the total distance)

Now the average speed taken to travel the total distance 3d in a total time of d/30+d/40+d/60 is were you could apply the formula to get the average speed S.

I hope that all makes sense, props to the gmatclub math book.
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Re: Rajesh traveled from home to school at 30 miles per hour. Then he retu   [#permalink] 19 Nov 2018, 16:07
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