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Valentine's Day

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by GmatKiss » Sat May 12, 2012 3:47 am
On Valentine's Day, a busy florist drove his delivery truck from Palm Beach to Miami at an average rate of 45 miles per hour. On his return trip to Palm Beach, he encountered rush hour traffic, which slowed him to an average speed of 25 miles per hour. What was the driver's average speed for the trip, in miles per hour?

a. 30
b. 32
c. 35
d. 36
e. 38
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by Birottam Dutta » Sat May 12, 2012 4:44 am
On Valentine's Day, a busy florist drove his delivery truck from Palm Beach to Miami at an average rate of 45 miles per hour. On his return trip to Palm Beach, he encountered rush hour traffic, which slowed him to an average speed of 25 miles per hour. What was the driver's average speed for the trip, in miles per hour?

a. 30
b. 32
c. 35
d. 36
e. 38

Average Speed = (Total Distance/Total Time)

Let the distance both says be d.

Therefore, total distance = 2d.

Time taken one way = d/45 and on return = d/25.

Therefore, total time = d/45 + d/25

So, average speed = 2d/ (d/45 + d/25)

On calculation, it comes out to be 225/7 which is approximately equal to 32.

Hence, b!
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by gmatblood » Sat May 12, 2012 6:03 am
Looking for expert's help.
Thanks
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by neelgandham » Sat May 12, 2012 9:18 am
Looking for a short cut or a POE solution ??(Let me know)

I reckon the solution by Birottam is the best and easiest ! #MyOpinion
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by GmatKiss » Sat May 12, 2012 12:44 pm
neelgandham wrote:Looking for a short cut or a POE solution ??(Let me know)

I reckon the solution by Birottam is the best and easiest ! #MyOpinion
Please let me know the short cut.

TIA,
GK
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by neelgandham » Sat May 12, 2012 1:06 pm
The only shortcut I know of is The average speed formula

Average speed S = [2*(S1)*(S2)]/[S1+S2] miles per hour. where S1,S2 are the speeds of the car/man travelling to/from the origin.

Average Speed S = 2*25*45/(25+45) = 32.x miles per hour

p.s: You can use this formula to calculate average speed in a round trip.
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by GMATGuruNY » Sat May 12, 2012 4:51 pm
GmatKiss wrote:On Valentine's Day, a busy florist drove his delivery truck from Palm Beach to Miami at an average rate of 45 miles per hour. On his return trip to Palm Beach, he encountered rush hour traffic, which slowed him to an average speed of 25 miles per hour. What was the driver's average speed for the trip, in miles per hour?

a. 30
b. 32
c. 35
d. 36
e. 38
The average speed here is not an integer value.
The question really should ask for the APPROXIMATE average speed.

The ratio of the TIMES there and back is the RECIPROCAL of the ratio of the RATES there and back.
Since the ratio of the rates there and back = 45:25 = 9:5, the ratio of the times there and back = 5:9.
Thus, of every 14 hours traveled, 5 hours will be at 45mph and 9 hours will be at 25mph.
Thus, the average speed for the whole trip = (5*45 + 9*25)/14 ≃ (225+225)/14 ≃ 32.

The correct answer is B.
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