front wheel and rear wheel of tractor?

Question

The front wheels of a tractor are 0.5 m in diameter and the rear wheels are 2 m in diameter.

whats the distance travelled by the tractor when the front wheel has revolved 2100 times more than the rear wheels ?

(1)8.8 km
(2)2.2 km
(3)5.28 km
(4)4.4 km


KINDLY ,PLEASE dont give soln, i want to solve myself, i want to take the challenge ....if i cant solve it , i will post it again ....but for the time being i need hints .

what i dont understand is , whats the relationship between front wheel and rear wheel ? i think the tractor will move the same distance .......whether the front wheel is bigger or smaller than the rear wheel ...it does not matter .

BY the way , as per the question , it asks how much distance tractor will move given a front wheel and real wheel revolution difference .

can you give me some HINTS so that i can use that in my head and proceed to solve ?

thank you

Mt Helmut,

I was also doing like that .....unless we have 2 eqn , we cant solve .

how do i frame 2 eqn ?

I tried this way ,

Let
n1 = no of revolutions of front wheel
n2 = no of revolutions of rear wheel

we are given n1-n2=2100 ...................(1)

we also Front wheel moves pi*.5*n1 and Rear wheel moves pi*2*n2

so if we are able to find n1 or n2 any one ...then we can substitute in above and get the distance.

But to do that we need one more eqn to frame and i am stuck there

-----------------
Finally solve it ,

got the answer 4.4 km.

thanks

Answer 1

Firstly, let me clarify your doubt that the front wheel and the back wheel of the tractor are different in size, so if the tractor moves a certain distance, the front wheel, being smaller, will make more revolutions compared ot the bigger back wheel.

If the back wheel makes "n" revolutions, the front wheel will have made "(n + 2100)" revolutions. In one revolution, the distance travelled will be the circumference of the wheel. So even though the number of revolutions made by the wheels will be different, the distance travelled will be the same as they are both connected to the same tractor. Now all you have to do is form an equation for this.

Answer 2

They are asking you to figure out the difference in tire size (if wheel x moves 2m, how many times does wheel y need to turn to move 2m), and then how much ground it covers

Answer 3

let n = number of revolutions of the rear tire.
d = distance traveled.
d = 2nπ = 0.5(n + 2100)π

Solve for n, then for d, or substitute d/(2π) for n and solve for d.

Answer 4

extremely tough stuff. try searching with a search engine. just that could actually help!