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Every evening, Mr. Ben walks around a square city block once. Beginning at a corner, he would walk the first three sides at 6 feet per second and the final side at 5 feet per second. What is his average speed in feet per second? Express your answer as an improper fraction.

 
gueesstt  Apr 14, 2018
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 #1
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Side 1    6 fps

         2   6 fps

         3   6 fps

         4   5 fps

 

Let x = distance of each side (it will cancel out)

 

x ft  / 6 ft/sec   x 3     +   x ft / 5ft/sec = 4x / (avg)

(3/6 sec + 1/5 sec ) x  = 4x / avg        Divide both sides by 'x'

15/30 + 6/30  = 4/avg                         Solve for avg  (which is average speed in ft/sec)

avg = 4 / (21/30) = 120/21 ft/sec = 40/7 ft/sec

 
ElectricPavlov  Apr 14, 2018
edited by ElectricPavlov  Apr 14, 2018
edited by ElectricPavlov  Apr 14, 2018
 #2
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Let the the length of each side of the square=D

Let the time it takes him to walk one side of the square =T

Then the time it takes him to walk 3 legs of the square =3T

D =6T x 3 = 18T - distance of the first 3 legs of his walk.

The time it takes him to walk the last leg of his walk =6/5T =1.2T

1.2T x 5 =6T - distance covered in the last leg

Total distance covered / Time taken = Average speed

[18T + 6T] / [3T + 1.2T] =24T / 4.2T =5 5/7 - feet/sec - his average speed around the block.

 
Guest Apr 14, 2018

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