Final answer:
The plumber and his assistant worked for 50 hours and 25 hours respectively on this job.
Step-by-step explanation:
To find out how long the plumber and his assistant worked on this job, we can set up a system of equations based on the given information. Let's denote the number of hours the plumber worked as x, and the number of hours the assistant worked as y. Since the plumber works twice as long as the assistant, we can write the equation x = 2y.
The labor charge on the final bill is $1875, which is the sum of the labor charges for the plumber and the assistant. The plumber charges $30 an hour, so the labor charge for the plumber is 30x. The assistant charges $15 an hour, so the labor charge for the assistant is 15y. Therefore, we have the equation 30x + 15y = 1875.
Solving this system of equations, we can substitute the first equation into the second equation to get 30(2y) + 15y = 1875. Simplifying the equation gives us 60y + 15y = 1875, which further simplifies to 75y = 1875. Dividing both sides of the equation by 75 gives us y = 25.
Since x = 2y, we can substitute y = 25 into the equation to get x = 2(25), which is x = 50. Therefore, the plumber and his assistant worked for 50 hours and 25 hours respectively on this job.