Rate

[Guest]

The time for the wheels of a vehicle to make one revolution is reduced by 1/22 of a second when the rate is increased by 15 miles per hour. Calculate rate of vehicle if the circumferences of the wheels are 6 feet.

[Guest]

1/22 second = .04545 seconds = .000012625 hours (converted to hours due to rate in hours).

6 feet = .00113636 miles (converted to miles due to rate in miles).

How do I proceed from here ?

[Guest]

15 x 5280 / 3600 = 22 feet per second increase in speed

Ratio of the increase in speed to original speed will equal the ratio of the reduction in time per rev. to the original rev. time.

Let S = original speed in feet per second.
Then Revs per second = (S / 6)
Let T = original Time for 1 rev of wheel. = (6 / S) seconds.

(22 / S) = (1/22) / (6 / S)

(22 / S) = ((1/22) x S) / 6

(22 / S) = (S) / (6 x 22)

S^2 = 6

S = 2.449 feet per second .. OR .. 1.67 miles per hour