Two companies working together can clear a parcel of land in 8 hrs. Working alone, it would take company A 2 hrs longer than company B. How long it would take company B to clear the parcel of land alone?
time=task/rate
timetogether=8hrs
timaA=timeB+2
joint time=timea+timeB=2timeb+2
8hours=2timeb+2 so solve for time B
Let's assume that Company B can clear the parcel of land alone in 'x' hours.
We know that two companies working together can clear the parcel of land in 8 hours. So, the combined work rate of Company A and Company B is 1/8 of the parcel of land per hour.
Now, according to the given condition, if Company A works alone, it takes them 2 hours longer than Company B to clear the parcel of land. This means that the work rate of Company A is 1/(x+2) of the parcel of land per hour.
The combined work rate of Company A and Company B is equal to the sum of their individual work rates, so we can set up the equation:
1/8 = 1/x + 1/(x+2)
To solve this equation, we can find a common denominator:
1/8 = [(x+2) + x] / (x(x+2))
We can then simplify the equation:
1/8 = (2x + 2) / (x(x+2))
Next, we can cross-multiply:
x(x+2) = 8(2x + 2)
Expanding both sides of the equation:
x^2 + 2x = 16x + 16
Now, let's bring all the terms to one side of the equation:
x^2 + 2x - 16x - 16 = 0
Simplifying further:
x^2 - 14x - 16 = 0
Now, we can solve the quadratic equation for x. Using factoring or the quadratic formula, we find that the two possible solutions are x = -1 and x = 16.
Since time cannot be negative, the only valid solution is x = 16. Therefore, it would take Company B 16 hours to clear the parcel of land alone.