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

Question

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

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

D3N0 · Answer

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.

CounterSniper · Answer

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

nigg777 · Answer

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.

Abhishek009 · Answer

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)

jalice · Answer

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)

rosmann · Answer

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  
 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.

MHIKER · Answer

Time =Distance/Rate; Let the distance is D

So, Total time taken =\frac{ D}{30}+\frac{D}{40}+\frac{D}{60}=\frac{9D}{120}=\frac{3D}{40}

Average \ Speed =\frac{Distance \ Traveled}{Time \ Taken}

=3D*\frac{40}{3D}=40

The answer is  C.

MHIKER · Answer

A very short of solving the PS is applying the following formula:

Average \ Speed = \frac{3abc}{(ab + bc + ca)}  
 This formula applicable when one travels three parts of distance at three different speeds.

Average \ Speed=\frac{3(30*40*60)}{30*40+40*60+60*30} = \frac{3(30*40*60)}{1200+2400+1800} = \frac{3(30*40*60)}{5400}

Average Speed=40

The answer is  C

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

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