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doubts in calculations

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by divya23 » Mon May 30, 2011 3:31 am
A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist's average speed for the round trip, in miles per hour?

1. 4 4/5
2. 5
3. 5 1/5
4. 5 2/5
5. 5 3/5
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by cans » Mon May 30, 2011 3:43 am
Distance = speed* time
Distance from a to b = 2*4 = 8 miles
thus time taken to travel back = distance/speed = 8/6 = 4/3 hr.
total time = 2+4/3 hr = 10/3 hr
Total distance = 8+8 = 16 miles
speed = distance/time = 16/(10/3) = 24/5 hr = 4 4/5
IMO A
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by divya23 » Mon May 30, 2011 3:47 am
yup its A..i forgot to cancel out ..many thanks :)
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by Anurag@Gurome » Mon May 30, 2011 8:07 pm
divya23 wrote:A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist's average speed for the round trip, in miles per hour?

1. 4 4/5
2. 5
3. 5 1/5
4. 5 2/5
5. 5 3/5

Solution
In such speed and distance problems, where we need to calculate the average speed, distance remaining the same, we can use the concept of harmonic mean.
Now the harmonic mean of two quantities 'a' and 'b' is 2ab/(a+b).
Here the average speed is the harmonic mean of 4 and 6 which is (2*4*6)/(4+6) = 4.8 = 4 4/5.

The correct answer is (1).
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by divya23 » Mon May 30, 2011 8:10 pm
Thank you
sumtimes v try to complex even d simplest of things
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by sivaelectric » Mon May 30, 2011 9:02 pm
Good explanation Cans and Anurag sir, and Divya, Yes! it happens that sometimes we complicate little things. :) But I got a little doubt here, whats the difficulty level of this question? May be say in the range of 350-450 range. Just curious to as its an easy one.
If I am wrong correct me :), If my post helped let me know by clicking the Thanks button ;).

Chitra Sivasankar Arunagiri
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