Question

To cover a distance of 160 m the front wheel
of a car rotates 12 times more than the back
wheel and the circumference of the front
wheel is 3 m less than the back wheel. Find
the circumference of each wheel.​

Answer 1

Step-by-step explanation:

The circumference of the front wheel of the cart = 30 ft.

The circumference of the rear wheel of the cart = 36 ft.

Let the rotations of the rear wheel be x. Then 36x = 30(x+5), or

36x = 30x + 150, or

6x = 150, or

x = 25.

So the rear wheel makes 25 rotations and the distance covered by the cart = 25*36 = 900 ft.

Answer 2

Answer:

Let the circumference of back wheel be x m.

so, the circumference of front wheel will be ' x-3 ' m.

now, to cover distance of 160 m

front wheel rotates = 160/(x-3)m

and, back wheel rotates = 160/x m

Again, according to question, front wheel rotates 12 times more than back wheel.

160/(x-3) - 160/x = 12

{160x - 160(x-3)} / x(x-3) = 12

160x - 160x + 480 = 12( x^2 - 3x )

480 = 12x^2 - 36x

12x^2 - 36x - 480 = 0

12 ( x^2 - 3x - 40 ) = 0

x^2 - 3x - 40 = 0

x^2 - 8x + 5x - 40 = 0

x(x-8) + 5(x-8) = 0

(x-8) (x+5) = 0

Either, x-8 = 0. Or, x+5 = 0

x = 8. x = -5.

value of x cannot be negative so, value of x = 8.

therefore, the circumference of back wheel is x=8 m

and, the circumference of front wheel is x-3=8-3=5m.