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Rajesh traveled from home to school at 30 miles per hour. Th
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18 Jun 2018, 14:49
18 Jun 2018, 14:49
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Question Stats:
80% (01:42) correct
20% (01:59) wrong based on 95 sessions
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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
(A) 32
(B) 36
(C) 40
(D) 45
(E) 47
Re: Rajesh traveled from home to school at 30 miles per hour. Th
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02 Jul 2018, 04:59
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
(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 = \(\frac{(3 * 30 * 40 * 60)}{(30 * 40 + 40 * 60 + 60 * 30)} = \frac{(3 * 30 * 40 * 60)}{5400} = 40 miles/hr\)
Re: Rajesh traveled from home to school at 30 miles per hour. Th
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07 Jul 2018, 04:51
07 Jul 2018, 04:51
3
Expert Reply
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.
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.
