Question

Worker A can a task in 9 hours while worker B can complete the same task in 4 hours. How long (in hr) would it take the workers to complete the task together? ( Enter an exact number as an integer, fraction, or decimal.)

Answer 1

Answer:   $\bold{\dfrac{36}{13}\ hours}$

Step-by-step explanation:

$Worker\ A: 1\ job\ in\ 9\ hours=\dfrac{1}{9}\\\\Worker\ B: 1\ job\ in\ 4\ hours=\dfrac{1}{4}\\\\Total: 1\ job\ in\ x\ hours=\dfrac{1}{x}\\\\\\Worker\ A+Worker\ B = Total\\\\\dfrac{1}{9}+\dfrac{1}{4}=\dfrac{1}{x}\\\\\dfrac{1}{9}(36x)+\dfrac{1}{4}(36x)=\dfrac{1}{x}(36x)\\\\4x + 9x = 36\\\\13x = 36\\\\.\ x=\dfrac{36}{13}\\\\.\quad =2\dfrac{10}{13}\ hours$