Emilie can complete a job in 10 minutes, while Erica can complete the same job in 15 minutes. How long would it take them to complete the job working together? (In minutes.) Rate of work problem.

9514 1404 393

  6 minutes

Step-by-step explanation:

The rates add when expressed in terms of jobs per minute.

  1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6

The two together can complete 1/6 jobs per minute, so it will take them 6 minutes to complete 1 job.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3