How long will it take the assistant?

Question

A scientist and her assistant, working together, can complete an experiment in 6 hours. Working alone, the scientist could complete the experiment in 9 hours. How long would it take the assistant to complete the experiment solo?

Answer 1

the workrate of the scientist is 1/9

the combined workrate is 1/6

1/x + 1/9 = 1/6

18 + 2x = 3x <--- multiplies both sides by 18x

18 = x

the assistant completes the experiment in 18 hours working alone.