00:00The radius of a tractor's large rear wheel is twice the radius of its smaller front wheel.
00:05If the smaller wheel makes 25 more revolutions than the larger wheel over a distance of 100 meters, what is the circumference of the smaller wheel in meters?
00:13Our friends are asking us this question.
00:15Now, friends, we know that the product of the number of revolutions and the diameter, or rather the circumference, is equal to the distance traveled, isn't it?
00:30Now let's look at the proportion and position of our smaller, front wheel and our larger, rear wheel.
00:47So, friends, what is the small wheel? Looking at it, it rotates 25 revolutions faster than the large wheel.
00:53If I say the rotational speed of the small wheel is x plus 25, then we will set up the following proportion for the large wheel.
01:03What would the radius of the large wheel, or rather its revolutions per minute, be? Wouldn't x be the answer? Yes, it would.
01:14So, what does "small" mean? The radius of the large wheel is twice the radius of the small wheel.
01:19So when we multiply this by r, and since it's twice as much, we multiply it by two r's, then friends, they are equal.
01:28will be.
01:29Well, isn't that also equivalent to a road?
01:34Yes, well, that's what my friends are saying, at a distance of 100 meters.
01:40Won't they both take a total of 100 meters? Yes, 100 is equal.
01:43Okay, now let's take a look at our proportions.
01:46R times x plus 25, which equals x times 2r.
01:50Let's look at this first.
01:51What can be simplified here? Right, folks? Yes.
01:54x plus 25 is equal to 2 times x.
01:57We find our x to be 25 from here.
02:01So, guys, this one does 50 revolutions per minute while this one does 25 revolutions per minute.
02:05So when we look at this, when we look at this big wheel, the rear wheel, friends...
02:09If our x is 25, and 25 multiplied by 2 multiplied by r equals 100, what can we find from this?
02:16We can now find its diameter, or rather, its circumference.
02:19That's what we'll think.
02:21When we divide by 50, both sides cancel out.
02:25We also accept our r from here, that is, as the environment.
02:29Because diameter and circumference are directly proportional, friends.
02:32That equals 2 meters.
02:36What is this? It's the circumference of a small wheel, folks.
02:39Our answer is Ceyhan 2.
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