Lesson Selected joint-work word problems from the archive

Selected joint-work word problems from the archive

Problem 1

Let x be the time the slower machine takes. Then the faster machine will take (x-2) hours.

Thus the rate-of-work of the slower machine is ,  while the rate-of-work of the faster machine is  .

The combined rate of two machines working together is   + .

According to the condition,

 +  = .    ( <---  =  hours = 2 hours and 24 minutes)

Or

 +  = .

It is your equation for x. To solve it, multiply both sides by 12*x*(x-2). You will get

12(x-2) + 12x = 5x*(x-2).

Now simplify and solve it:

12x - 24 + 12x = .

 = .

Apply the quadratic formula and find the positive root x = 6.

Answer. 6 hours.

Problem 2

Let D = time needed for David to complete the job, in hours, and
let J = time needed for Jodi  to complete the job.

According to the condition, 

D = J - 6.     (1)

David's rate-of-work is ; Jodi''s rate-of-work is .

Their combined rate-of-work is .

According to the condition, 

 = .   (2)     ( <---  = )

Now substitute (1) into (2) and simplify the right side in (2). You will get

 = .    (3)

To solve (3), multiply both sides by 40*J*(j-6). You will get

40J + 40*(J-6) = 3*J*(J-6).

Simplify and solve it:

 = ,

 = .

Apply the quadratic formula to get the roots.

They are  and .

Notice that the solution for Jody must be greater than 6 hours, in order J-6 was meaningful. 

It gives the only solution of 30 hours for Jody and D = J-6 = 24 hours for David.

Problem 3

Your equation is 


 = .


 is the rate of work of the first man.
 is the rate of work of the second man.

 is their combined rate of work.

To solve (1), multiply both sides by 5*x*(x+1). You will get

5(x+1) + 5x = x*(x+1).

Simplify and solve 

 = ,

 = .

Now apply the quadratic formula to find the solution.