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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # Rajesh traveled from home to school at 30 miles per hour. Th  Question banks Downloads My Bookmarks Reviews Important topics
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TAGS: Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Rajesh traveled from home to school at 30 miles per hour. Th [#permalink]
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Expert's post 00:00

Question Stats: 80% (01:29) correct 20% (01:35) wrong based on 40 sessions
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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Sandy
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Re: Rajesh traveled from home to school at 30 miles per hour. Th [#permalink]
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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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GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3033  , given: 394

Re: Rajesh traveled from home to school at 30 miles per hour. Th [#permalink]
1
KUDOS
Expert's post
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]
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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