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.
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
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.