Question

The difference between the radius of the front wheel and the rear wheel of a tractor is \(2\) feet .
The ratio of the number of the revolutions made by the front and rear wheels of the tractor in a journey of \(13200\) feet is \(5:3\).
How many more revolutions are made by the front wheel than rear wheel in the whole journey.

Answer 1

@campbell_st

Answer 2

this might be useful

\(\large \color{black}{\begin{align}
f-r=2\\~\\
\dfrac{m(2\pi f )}{n(2\pi r)}=\dfrac{5}{3}\\~\\
\end{align}}\)

Answer 3

well both wheels travel 13200 ft... let r be the radius of the rear

so the rear revolutions are is 13200/2pir front revolutions 13200/2pi(r - 2)

so then given the ratio

5 : 3


13200 13200
-------- : ------
2pi(r -2) 2pi r


there you go... thats a start

Answer 4

\(\large \color{black}{\begin{align}
\dfrac{\dfrac{13200}{2\pi (r+2)}}{\dfrac{13200}{2\pi (r)}}=\dfrac{5}{3}\hspace{.33em}\\~\\
\end{align}}\)

is this correct?

Answer 5

@Michele_Laino

Answer 6

I think that the problem can be modeled by the subsequent equations:
\[\left\{ \begin{gathered}
D = d + 4 \hfill \\
\frac{N}{n} = \frac{5}{3} \hfill \\
ND = nd \hfill \\
\pi DN = 13200 \hfill \\
\end{gathered} \right.\]

Answer 7

where D, N are the diameter and the frequency of the front wheel, whereas d, and n are the correspondent quantities of the rear wheel

Answer 8

frequency ?

Answer 9

number of revolutions per second

Answer 10

oops...where D, N are the diameter and the frequency of the rear wheel, whereas d, and n are the correspondent quantities of the front wheel

Answer 11

d and n means which quantities ?

Answer 12

d and n are the diameter and the frequency of the front wheel