11th Grade Pre-Calc

Question

A new copying machine can do a certain job in one hour less than an older copier. Together they can do this job in 1.2 hours. How many minutes would it take the older copier by itself to do the job? How many minutes would it take the newer copier to do the job?

Answer 1

Hi Carson

 

Let call T_A the spent time by the older machine to finish a job

 

Let call T_B the spent time by the newer machine to finish the same job done by the older one.

 

We already know that:  T_B = T_A - 1 hr.    (1)

 

Also, we know that:   T_B + T_A = 1.2 hrs.  (2)

 

The expressions (1) and (2) form a linear equation system with two unknowns (T_A and T_B). You can use different methods to resolve it, but I will apply the substitution method for convenience.

 

Then I will use the expression (1) for T_B  for replacing it in expression (2):

 

(T_A - 1) + T_A = 1.2

 

2T_A = 1 + 1.2    or,     T_A = 2.2/2  = 1.1 hrs. = 72 minutes

 

Then, from expression (1) :   T_B = T_A - 1  = 1.1 - 1 = 0.1 hrs =  6 minutes

 

I hope it helps you.

Answer 2

Let x = number of hours for the old copier to do the job alone

 

Then x-1 = number of hours for the new copier to do the job alone

 

1/x = amount of job done by old copier each hour

 

1/(x-1) = amount of job done by new copier each hour

 

1/1.2 = 5/6 = amount of job done per hour if both copiers are used

 

Then, 1/x + 1/(x-1) = 5/6

 

Multiply by the LCD, 6x(x-1):  6(x-1) + 6x = 5x(x-1)

 

                                                12x - 6 = 5x² - 5x

 

                                         5x² - 17x + 6 = 0

 

                                         (5x-2)(x-3) = 0

 

                                            x = 2/5 or x = 3

 

x can't be 2/5 (Otherwise, x-1 is negative)  So, x = 3 hours

 

                                                                     = 180 minutes

 

Number of minutes for the newer copier = 120 minutes