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Question
The diameters of the front and the rear wheels of a tractor are 63 cm and 1.54 m respectively. The rear wheel is rotating at `24 6/11` revolutions per minute. Find:
(i) the revolutions per minute made by the front wheel.
(ii) the distance traveled bu the tractor in 40 minutes.
Solution
Given the diameter of the front and rear wheels are 63 cm = 0.63 m and 1.54 m respectively,
The radius of the rear wheel = `1.54/2` = 0.77 m.
and radius of the front wheel = `0.63/2` = 0.315 m
Distance traveled by tractor in one revolution of the rear wheel = circumference of the rear wheel
= 2πr
= 2 x `22/7` x 0.77
= 4.84 m
The rear wheel rotates at `24 6/11` revolutions per minute
= `270/11` revolutions per minute
Since in one revolution, the distance traveled by the rear wheel = 4.84 m
So, in `270/11` revolutions, the tractor travels `270/11` x 4.84 = 118.8 m
Let the number of revolutions made by the front wheel be x.
(i) Now, the number of revolutions made by the front wheel in one minute x circumference of the wheel
= the distance traveled by tractor in one minute
⇒ `x xx 2 xx 22/7 xx 0.315 = 118.8`
⇒ `xx = [ 118.8 xx 7 ]/[ 2 xx 22 xx 0.315 ]` = 60
(ii) Distance traveled by tractor in 40 minutes
= number of revolutions made by the rear wheel in 40 minutes
x circumferent of the rear wheel
= `270/11 xx 40 xx 4.84 = 4752` m
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