the company found that an experienced surveyor can survey a roadbed in 5 hours:

1/5 survey per hour the rate of the experienced surveyor

an apprentice surveyor needs 11 hours to survey the same stretch of road:

1/11 survey per hour the rate of the apprentice surveyor

let 'x' represent the number of hours the experienced surveyor and the apprentice surveyor need to complete the job together

1/x survey per hour the together rate

1/5 + 1/11 = 1/x

by solving we find:

x = 55/16

x = 3 7/16 hr

x = 3 hr 7*60/16 min

x = 3 hr 26 min 4*60/16 s

x = 3 hr 26 min 25 s

click here to see the step by step solution of the equation:

they will need 3 hr 26 min 25 s to complete the job together.