Question

for a project, it takes john 10 days to complete alone, and 8 days for john and tony to complete together. then tony needs days to complete this project alone.

Explanation:

Step1: Define work rates

Let total work = 1. John's rate: $\frac{1}{10}$ per day. Combined rate: $\frac{1}{8}$ per day.

Step2: Find Tony's work rate

Tony's rate = Combined rate - John's rate
$\text{Tony's rate} = \frac{1}{8} - \frac{1}{10} = \frac{5-4}{40} = \frac{1}{40}$

Step3: Calculate Tony's time alone

Time = $\frac{\text{Total work}}{\text{Tony's rate}} = \frac{1}{\frac{1}{40}}$

Answer:

40