SOLUTION: Bill's bike wheels have a 26-in. diameter. The odometer on his bike counts the number of times a wheel rotates during a trip. If the odometer counts 200 rotations during the trip f

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Question 1204230: Bill's bike wheels have a 26-in. diameter. The odometer on his bike counts the number of times a wheel rotates during a trip. If the odometer counts 200 rotations during the trip from Bill's house to school, how many feet does Bill travel? Round to the nearest foot.
Found 4 solutions by josgarithmetic, MathLover1, math_tutor2020, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
c%2F26=pi
c=26%2Api-----------length of 1 rotation

200%2A26%2Api%2Ainches----------distance for those two hundred rotations, but in inches. You want in feet.


%28200%2A26%2Api%29%2F12--------the amount in feet. Compute that.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
diameter d=26in
One rotation is same distance as:
+pi%2Ad+=+3.14%2A26+=+81.64in
Total distance traveled:
If the odometer counts 200 rotations, we have

200%2A81.64+=+16328in
Convert inches to feet:
12in+=+1ft
16328in+=%28+16328%2F12%29ft+=+1360.66666667ft ≈ 1361ft


Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: 1361 feet

Explanation

d = diameter = 26 inches
C = circumference = perimeter around the circle

C = pi*d
C = 3.14*26
C = 81.64
This is the approximate distance around the wheel. It's approximate because pi = 3.14 is approximate.
Use more decimal digits of pi to get a better approximation.


1 full rotation of the wheel will move the bike forward roughly 81.64 inches.
This assumes that there isn't any slipping. Slipping is when the wheel spins some amount different compared to how the bike moves. Example: the wheel rotates 5 feet but the bike only would move forward 2 feet.

200 such rotations would move the bike forward 200*81.64 = 16,328 inches.

Divide by 12 to go from inches to feet
16328/12 = 1,360.66666666667 approximately

When rounding to the nearest foot we get 1361 feet as the final answer.


As a shortcut, we can type this into the calculator
pi*26*200/12
where we let the calculator handle the decimal digits of pi for the best accuracy possible.
The result of which is approximately 1,361.35681655558 which rounds to 1361 feet
Either way we'll get the same answer.

Side note: 1361 ft = 1361/5280 = 0.2578 miles approximately

Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.

how many feet = pi%2Ad%2Arotations = 3.14159%2A26%2A200 inches = 16336.27 inches = 16336.27%2F12 feet = 1361 feet (rounded to the nearest foot).    ANSWER

Solved.