Question 1139833: A carabao can plough a farmer's land in 6 hours. A tractor can plough the land in 4 hours. The farmer used the carabao to plough the land for 2 hours, after which, another farmer decided to help him using the tractor. How long did it take the farmers tofinish ploughing the land?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! r * t = q
r is the rate
t is the time
q is the quantity.
the quantity in this case is one ploughed field.
the carabao can do it in 6 hours, therefore r * t = q becomes r * 6 = 1.
solve for r to get r = 1/6.
the tractor can do it in 4 hours, therefore r * t = q becomes r * 4 = 1.
solve for r to get r = 1/4.
the rate of the carabao is 1/6 of the field in 1 hour.
the rate of the tractor is 1/4 of the field in 1 hour.
the farmer uses the carabao to plough the field for 2 hours.
r * t = q becomes 1/6 * 2 = q.
solve for q to get q = 1/6 * 2 = 1/6 = 1/3.
in 2 hours, the farmer has ploughed 1/3 of the field.
that leave 2/3 of the field to still be ploughed.
another farmer decides to help him using the tractor.
the last 2/3 of the field is then ploughed using the carabao and the tractor.
when both are used, their rates are additive.
the formula of r * t = q becomes (1/6 + 1/4) * t = 2/3
simplify to get 5/12 * t = 2/3
solve for t to get t = 2/3 * 12/5 = 8/5.
the remaining 2/3 of the field is ploughed in 8/5 = 1 and 3/5 hours.
that's your solution.
r * t = q becomes 1/6 * 2 + 5/12 * 8/5 = q
1/6 * 2 is with the carabao only.
5/12 * 8/5 is with both the carabao and the tractor.
solve for q to get q = 1
the whole field is ploughed in 2 hours and 8/5 hours = 3 and 3/5 hours.
that was 2 hours using the carabao and 1 and 3/5 hours using both the tractor and the carabao.
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