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Rajesh traveled from home to school at 30 miles per hour. Th

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Rajesh traveled from home to school at 30 miles per hour. Th [#permalink] New post 18 Jun 2018, 14:49
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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
[Reveal] Spoiler: OA

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Re: Rajesh traveled from home to school at 30 miles per hour. Th [#permalink] New post 02 Jul 2018, 04:59
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sandy 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



Remember for 3 speeds given and we need to find the av. speed, then we can use the formula: \(\frac{3abc}{(ab + bc + ca)}\), where a,b and c are 3 speeds given.

In this problem let us take a = 30miles/hr, b= 40miles/hr , c = 60 miles/hr

Therefore the av. speed = \(\frac{(3 * 30 * 40 * 60)}{(30 * 40 + 40 * 60 + 60 * 30)} = \frac{(3 * 30 * 40 * 60)}{5400} = 40 miles/hr\)
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Re: Rajesh traveled from home to school at 30 miles per hour. Th [#permalink] New post 07 Jul 2018, 04:51
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Explanation

Do not just average the three speeds, as Rajesh spent more time at slower rates than at higher rates, weighting the average toward the slower rate(s). To compute the average speed for a trip, figure out the total distance and divide by the total time.

Pick a convenient distance from home to school, one that is divisible by 30, 40, and 60—say 120 miles (tough for Rajesh, but easier for you).

The first part of the journey (from home to school) took \(\frac{120}{30}= 4\) hours.

The second part of the journey took \(\frac{120}{40}= 3\) hours.

The third part of the journey took \(\frac{120}{60}= 2\) hours.

The total distance Rajesh traveled is 120 + 120 + 120 = 360 miles.

The total time was 4 + 3 + 2 = 9 hours. Finally, his average speed for the entire trip was = 40 miles per hour.
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Re: Rajesh traveled from home to school at 30 miles per hour. Th [#permalink] New post 09 Jul 2019, 06:04
sandy 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



The easy way: let distance =\(d\).

Total distance: \(d+d+d\)(going+coming+again going) = \(3d\) .

R travel" \(\frac{d}{30}\); then return \(\frac{d}{40}\); again went to school \(\frac{d}{60}\).
So total travel \(\frac{d}{30}\)+\(\frac{d}{40}\)+\(\frac{d}{60}\).

We may calculate that the LCM of \(30,40,60\) is \(120\).

So \(\frac{d}{30}\)+\(\frac{d}{40}\)+\(\frac{d}{60}\) = \(\frac{4d + 3d + 2d}{120}\) =\(\frac{9d}{120}\)

So, \(\frac{3d}{(9d/120)}\) = \(3d\) *\(\frac{120}{9d}\) = \(40\) hour per mile.

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Re: Rajesh traveled from home to school at 30 miles per hour. Th   [#permalink] 09 Jul 2019, 06:04
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