Translate the following into an algebraic expression: if mr. david does a job in x hours and mr. ludwig in y hours. what part of the job they could do together if they worked for k hrs?

For this case we have the following variables:

x: number of hours that it takes Mr. David to complete a job working alone.

y: number of hours it takes Mr. Ludwing to complete a job working alone.

k: number of hours it takes for both of them to do a job working together.

We now write the equation that models the problem.

To do this, we must add the work rate per hour of each and equal to the rate of work per hour of both.

We have then:

The algebraic expression that models the problem is:

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50

the answer is 31.27mph