Two bulldozers clear homes from a 20-acre tract of land. One works twice as fast as the other. It takes them three days to clear the tract working together. How long would it take each of them alone?
whats the equation?
To find the equation for this problem, we need to understand that the rate at which work is done is inversely proportional to the time it takes to complete the work. Let's break down the problem step by step:
Let's say one bulldozer's rate is "x" acres per day, and the other bulldozer's rate is "2x" acres per day, as it works twice as fast.
So, in one day, the first bulldozer can clear x acres, and the second bulldozer can clear 2x acres.
Working together for three days, the total work completed is the product of their combined rates and the time (3 days):
3 * (x + 2x) = 20
Simplifying the equation, we get:
3 * 3x = 20
9x = 20
Now, we can solve for x, which represents the rate of the slower bulldozer:
x = 20/9
The rate of the slower bulldozer is 20/9 acres per day.
Since the rate of the slower bulldozer is x acres per day, it would take it 9/20 of a day to clear one acre:
1 acre / (20/9 acres per day) = 9/20 day
To find how long it would take the slower bulldozer to clear the whole 20-acre tract alone, we multiply the time per acre by the total area:
(9/20 day) * 20 acres = 9 days
So, it would take the slower bulldozer 9 days to clear the tract alone.
Since the rate of the faster bulldozer is 2x acres per day, it would take it half the time compared to the slower bulldozer to clear the land:
9 days / 2 = 4.5 days
Therefore, it would take the faster bulldozer 4.5 days to clear the tract alone.