The front wheel of a wagon makes 6 more revolutions than the rear wheel in trave

Question

The front wheel of a wagon makes 6 more revolutions than the rear wheel in traveling 36 feet. If the radius of each wheel were 2 inches more, the front wheel would make only a more revolutions than the rear wheel in traveling 36 feet. Find the circumference of each wheel.Ar Revorution5 made Lywhah i n CiRCUMF of eeae haelr At noon, Cathy begins to travel north at a constant rate. Three hours later, Kathy begins to travel north from a point 4 miles south of where Cathy started. Kathy's speed is steady during each one hour period, and forms an arithmetic progression hour by hour. Three hours after Kathy starts, she is traveling at twice Cathy's speed and has halved the distance that was between her and Cathy at 3:00pm. Four hours after Kathy starts, she catches up with Cathy. How fast does Cathy travel, and how fast is Kathy traveling when she catches up with Cathy?

Explanation / Answer

Front makes 6 more revs than the rear when travelling 36 ft.

No of revs made = distance travelled / circumference

So, we have
36/(2pi*r) - 36/(2pi*R) = 6
18/(pi*r) - 18/(pi*R) = 6
3/(pi*r) - 3/(pi*R) = 1

Now, second case :
2inches = 2/12 = 1/6 ft
36/(2pi*(r+1/6)) - 36/(2pi*(R+1/6)) = 3

Simplifying :
6/(pi*(r+1/6)) - 6/(pi(R+1/6)) = 1

We can solve those simultaneously....

We get r = 1/3 approx
and R = 1/2 approx

So, the radii are 4 inches and 6 inches

LArger wheel circumference = 2pi*4 = 8pi inches

Smaller wheel circum = 2pi*6 = 12pi inches

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