Please help -word problem

Question

One computer can solve a certain problem in 30 min. With the aid of a second computer the problem is solved in 10 min. How long would it take for the second

computer to solve the problem alone?

Answer 1

Jazz,

 

Work problems sometimes confuse students because you have to work in fractions.  If the first computer can do the job in 30 minutes, that means that each minute, the computer is doing 1/30 of the total job.  If the two computers combined can do the job in 10 minutes, each minute the team is doing 1/10 of the total job.  Setup the equation as given, then solve for x.

 

 1  +  1 = 1

30     x    10      [Multiply the entire equation by 30x (the least common denominator)

x+30=3x

30=4x

7.5=x               [This means the second computer could do the job alone in 7.5 minutes]

 

I hope this helps.

Answer 2

Let x = number of minutes it takes the 2nd computer to do the job                  alone

 

1/30 = work done by first computer in 1 minute if working alone

1/x = work done by second computer in 1 minute if working alone

1/10 = work done by both computers in 1 minute

 

1/30 + 1/x = 1/10

 

Multiply both sides by 30x:  x + 30 = 3x

                                              30 = 2x

                                                         x = 15 minutes

 

 

Answer 3

The first computer can solve a problem in 30 minutes. This means that for each minute the computer works, its solves 1/30 of the problem.

 

When the two computers work together, they can solve a problem in 10 minutes. This means that for each minute the computers work, they solve 1/10 of the problem.

 

So, 1/30 + 2nd computer's rate = 1/10.

 

Let's call the 2nd computer's rate "r".

 

1/30 + r = 1/10

 

r = 1/10 - 1/30

 

r = 3/30 - 1/30 

 

r = 2/30

 

r = 1/15

 

Using the reverse strategy that we used above, the second computer completes 1/15 of the job per minute... so the second computer must be working for 15 minutes.