SOLUTION: A forewheel of a carrier makes 6 revolution more than the rear wheel in going 120meter. If the diameter of fore wheel be increased by 1/4th it's present duameter and diameter of r

Click here to see ALL problems on Rate-of-work-word-problems

Question 1066546: A forewheel of a carrier makes 6 revolution more than the rear wheel in going 120meter. If the diameter of fore wheel be increased by 1/4th it's present duameter and diameter of rearwheel increases by 1/5th ot it's present diameter . The forewheel will make 4 revolution than rearwheel in same direction? Find the circumference.
Found 2 solutions by rothauserc, Alan3354:
Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
We have two equations in two unknowns
:
let d(1) be the diameter of the fore wheel
let d(2) be the diameter of the rear wheel
:
the circumference(C) of each wheel equals one revolution
:
the carrier goes 120 meters, then
:
1) (120 / (pi * d(1)) = (120 / (pi * d2)) + 6
2) (120 / (pi * 5 * d(1) / 4)) = (120 / (pi * 6 * d(2) / 5) + 4
:
simplify each equation
:
3) (20 * d(2)) = (20 * d(1)) + (d(1) * d(2) * pi)
4) (24 * d(2)) = (25 * d(1)) + (d(1) * (d(2) * pi)
:
solve equations 3 for d(1)
:
d(1) = (20 * d(2)) / (20 + d(2) * pi)
:
substitute for d(1) in equation 4
:
(24 * d(2)) = (25 + d(2) * pi) * (20 * d(2)) / (20 + d(2) * pi)
:
solve for d(2)
:
************************************************
d(2) = 5 / pi
d(1) = (20 * 5/pi) / (20 + (5/pi) * pi) = 4 / pi
:
C of fore wheel is pi * d(1) = 4 meters
C of rear wheel is pi * d(2) = 5 meters
************************************************
:
check answer
:
using equation 1 we have
:
(120 / 4) = (120 / 5) + 6
30 = 24 + 6 = 30
equation 1 checks
:
using equation 2
:
(120 / 5) = (120 / 6 ) + 4
:
24 = 20 + 4 = 24
equation 2 checks
:

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
A forewheel of a carrier makes 6 revolution more than the rear wheel in going 120meter. If the diameter of fore wheel be increased by 1/4th it's present duameter and diameter of rearwheel increases by 1/5th ot it's present diameter . The forewheel will make 4 revolution than rearwheel in same direction? Find the circumference.
---------------
Not 1/4th or 1/5th.
Either one 4th, or 1/4. Not 1/4th
==============
it's = it is