How long in hours is the entire practice ?

Question

A volleyball coach plans her daily practices to include 10 minutes of stretching,2/3 of the entire practice scrimmaging, and the remaining practice time working on drills of specific skills. On Wednesday, the coach planned 100 minutes of stretching and scrimmaging, how long in hours is the entire practice

Answer 1

Answer requested is in hours.  135 is in minutes, which easily could be converted as follows:

 

135 min.(hr./60 min.) = 2-1/4 hours.

 

My solution for number of minutes is as follows:

 

2x/3 + 10 = 100

 

2x/3         = 90

 

(3/2)2x/3  = 3(90)/2

 

                = 135

Answer 2

The entire practice is 2.25 hours long.

Answer 3

The key to word (story) problems is to correctly translate the words into concise, precise math expressions (variables and operations).

 

First, assign variables.  Try to include the one we are asked to report.

     Let T = total length of entire practice in hours

     Let A = time stretching in minutes

     Let B = time scrimmaging in minutes

     Let D = drills in minutes

 

Then, translate:

  "10 minutes of stretching"    means   A = 10    (eq1)

  "2/3 of the entire practice scrimmaging"    means   (2/3)*T = B   (eq2)

                                            (note:  "of" means multiply)

  "remaining practice time working on drills of specific skills"

         means    D = T - A - B     (eq3)     (total minus others)

  "100 minutes of stretching and scrimmaging"     means  100 = A + B     (eq4)

  "how long in hours is the entire practice"     means       report T

 

Now, the easy math:

  Put the value of A from eq1 into eq4 to find P

           100 = 10 + B

             90 = B              (subtract P from both sides)

  Now, we can put that value of B into eq2 to find T

            (2/3)*T = 90

                  T = (3/2)*90          (multiply both sides by (3/2)

                  T = 135 minutes = 2 hours 15 minutes

 

But, we have not found D (but then, the problem didn't ask us to).  Let's find it to check our answer (very important).

Put T,A, and B into eq3.  D = 35.

 

Final check:

   Is   10 + (2/3)135 +  35 = 135  ?   yes.

   Is    (2/3)135 = 90  ?    yes