Question

2. The forewheel of a carriage makes 6 revolutions more than the rearwheel in going 120 m. If the diameter of the forewheel be increased by 1 its present diameter and the diameter of the rearwheel be increased 4 by one fifth of its present diameter then the forewheel makes 4 revolutions more than the rearwheel in going the same distance (120 m). Find the circumference of each wheel of the carriage.​

Answer 1

Answer:

Let the diameter of the forewheel and rear wheel be d1 and d2 respectively.The circumference of each wheel = 1 revolution.

if the carrier goes 120m then,

120/ πd1 = 120/πd2 + 6  → (1)

120/π 5d1 /4= 120/ *6 πd2/5 + 4      → (2)

simplifying each of the equations we get,

20*d2 = (20 d1 + d1*d2 *π)   →(3)

24 d2 = (25d1+d2*d1*π)    → (4)

solving (3) and (1)

d1 = (20*d2/(20+d2*π)

substitute d1 in eq 4

(24*d2)= (25 *d2*π*(20*d2/(20+d2*π)

solve for d2 now,  

d2 =5/ π

d1= (20/5π)/ (20 +(5/π)*π) = 4/π

circumference c for forewheel is π*d1 = 4m

c for rear wheel is πd2 = 5m