Question

when the pedal onn a bike has turned 3 times in fourth gear, the rear wheel has turned 7 times. when the pedal has turned 12 times, how many times has the rear wheek turned?

Answer 1

7/3 = rear/2
3rear = 14
rear = 14/3 or 4 2/3 turns

or

3 pedal turns = 7 rears
1 pedal turn = 7/3 rears
2 pedal turns = 14/3 rears

Answer 2

The number of rotations of the rear wheel is directly proportional to the number of rotations of the pedal.

Therefore, if

`x` - the number of rotations of the pedal

`y` - the number of rotations of the rear wheel

then
`y=kx`

If
`x=3,y=7`, then

`7=3k\\\\k=(7)/(3)`

So
`y=(7)/(3)x`.

If
`x=12`, then

`y=(7)/(3)\cdot12=28`

So the rear wheel has turned 28 times.