The first programmer can write an app in 10 days. The second programmer can finish the same job in 8 days. How long would it take them to finish the job if they were working together?

Answer: 40/9 days

Step-by-step explanation: let x be the time when they work together

daily rate of the first programmer = 1/10

daily rate of the second programmer = 1/8

daily rate when they work together = 1/x

Therefore:

1/10 + 1/8 = 1/x

solving the equation:

9/40 = 1/x

x = 40/9

4 4/9 days.

Step-by-step explanation:

You work in rates per day, so:

1/10 + 1/8 = 1/x where x is the number of days working together.

Multiply through by the LCD 40x:

4x + 5x = 40

9x = 40

x = 40/9 = 4 4/9 days.