A man digs a trench in 3 days, another man can dig it in 5 days and a third man can dig it in 6 days working alone. How much time will they dig together?

Question

A man digs a trench in 3 days, another man can dig it in 5 days and a third man can dig it in 6 days working alone. How much time will they take to dig it together?

Answer 1

Let t = the time it will take them if they dig together

(time together)/(time alone) + (time together)/(time alone) + (time together)/(time alone) = 1

t/3 + t/5 + t/6 = 1   Multiply the entire equation by the LCD, which is 30.

10t + 6t + 5t = 30

21t = 30

t = 1.43 days, rounded to the nearest hundredth