Question 206942
    two technicians can complete a mailing in 3 hours when working together. alone, one can complete the mailing 2 hours faster than the other. how long will it take each person to complete the mailing alone? compute answer to two decimal places.
.
Let x = time it takes to complete mailing by slower tech
then
x-2 = time it takes by faster tech
.
3(1/x + 1/(x-2)) = 1
3/x + 3/(x-2) = 1
Multiply both sides by a common denominator x(x-2):
3(x-2) + 3x = x(x-2)
3x-6 + 3x = x^2-2x
6x-6 = x^2-2x
-6 = x^2-8x
0 = x^2-8x+6
Solve using the quadratic equation yields:
x = {7.16, 0.84}
We can throw out the 0.84 solution because it will give a negative answer for the faster tech leaving us with:
x = 7.16 hours for the slower tech
x-2 = 7.16-2 = 5.16 hours for the faster tech
.
Details of quadratic follows:
*[invoke quadratic "x", 1, -8, 6 ]