Question

At what speed in miles per hour will a bicycle travel if the rider can cause the 26-inch diameter wheel to rotate 90 revolutions per minute

Answer 1

26' wheel @ 90 rpms = 2,340 inches / min (26 x 90)

2,340 inches / min = 140,400 inches / hour (2,340 x 60)

140,400 inches / hour = 11,700 feet / hour (140,400 / 12)

11,700 feet / hour = approx. 2.216 miles / hour (11,700 / 5,280)

Answer 2

Speed of the bicycle is 6.96 miles per hour.

Explanation:

Diameter of the wheel = 26 inches

Rotation of the wheel = 90 revolution per minute

We have to calculate the speed of the bicycle.

Since in one rotation distance moved by the bicycle = circumference of the wheel

Distance traveled in one rotation = 2πr

=
`2* (3.14)((26)/(3))`

= 2×3.14×13

= 81.64 inch

Since rotation of the wheel is = 90 revolutions per minute

Therefore, speed of the bicycle = 90×81.64 inches per minute

= 7347.6 inches per minute

Since 1 inch =
`(1)/(63360)` miles

Therefore, 7347.6 inches =
`(7347.6)/(63360)` miles

= 0.116 miles per minute

`0.116\frac{\text{Miles}}{\text{Minutes}}=0.116* 60\frac{\text{miles}}{\text{hours}}`

= 6.96 miles per hour

Therefore, Speed of the bicycle is 6.96 miles per hour.