*RT*=

*J*where

*R*= rate,

*T*= time and

*J*= job(s)

**rate**(

*R*) can be calculated since we know her

_{S}**time**(

*T*) to complete the task is

_{S}**5 hours**and there is one

**job**(or task) so

*J*is

**1**.

*R*(5) = 1.

_{S}*R*(5) = 1 Dividing both sides by 5 we get

_{S}*R*= 1/5

_{S}**rate**(

*R*) can be calculated since we know his time (

_{B}*T*) to complete the task is

_{B}**4 hours**and there is one

**job**(or task) so

*J*is

**1**.

*R*(4) = 1.

_{B}*R*(4) = 1 Dividing both sides by 4 we get

_{B}4 4

*R*= 1/4

_{B}*R*+

_{S}T_{S}*R*=

_{B}T_{B}*J*

*T*is 2. Substituting we get:

_{B}*T*+ (1/4)(2) = (1)

_{S}*T*+ 1/2 = 1 [Multiplying (1/4)(2)]

_{S}*T*= 1/2 [Subtracting 1/2 from both sides]

_{S}*T*= 5/2 or 2.5 [Multiplying both sides by 5]

_{S}To answer the question, Sarah must work an extra 1/2 (or 0.5) hour(s) to complete the task (5/2 - 2 = 1/2 -

**or**- 2.5 - 2 = 0.5).

Steven B.

*R*+

_{S}T_{S}*R*=

_{B}T_{B}*J*

*T*(1/4)

_{S}+*T*Substitute for rates and job.

_{B}= 1*T*=

_{S}*T*, so substituting we get:

_{B}*T*(1/4)(

_{S}+*T*) = 1

_{S}*T*+ (1/4)(

_{S}*T*]) = 20(1)

_{S}*T*+ 5

_{S}*T*= 20 Distribute (and simplify)

_{S}*T*= 20 Adding (since they are both

_{S}*T*)

_{S}*T*

*= 20*

_{S}*T*= 20/9 and since

_{S}*T*=

_{B}*T*,

_{S}*T*= 20/9

_{B}*RT*=

*D*, rate x time = distance) or mixture (PQ = S, where P = %, Q = Quantity and S = Solution, although this one is a little more complicated than that). Often you will need to write 2 (or more) equation that can then be manipulated and combined (usually by substitution) to arrive at one equation in one variable (for example, in the 2nd problem, the 1st two equations are added together and then we had to write a third equation

*T*=

_{B}*T*in order to substitute and arrive at a new equation with just one variable in it).

_{S}04/24/14

Steven B.

04/24/14

Steven B.

*RT*=

*D*where

*R*= Rate,

*T*= Time and

*D*= Distance. And the mixture formula

*P*

_{1}

*Q*

_{1}+

*P*

_{2}

*Q*

_{2}=

*P*

_{3}(

*Q*

_{1 }+

*Q*

_{2})]. Anyway...

*R*+

_{S}T_{S}*R*=

_{B}T_{B}*J*Starting from here...

*T*+ (1/4)

_{S}*T*= (1) Now we have a problem, because we have one equation with 2 variables in it

_{B}*T*=

_{S}*T*.

_{B}*T*+ (1/4)

_{S}*T*= (1) Substituting

_{S}*T*for

_{S}*T*.

_{B}*T*+ (1/4)

_{S}*T*] = 20(1) x20 which gives us...

_{S}*T*+ 5

_{S}*T*= 20 Next we add the like terms...

_{S}*T*= 20 Now dividing both sides by 9

_{S}*T*= 20/9 = 2 & 2/9 hrs.

_{S}**or**2.2222... hrs.

**or**≈ 2.22 hrs. (

**or**2 hour 13 & 1/3... min., etc. etc. etc.)

*T*= 20/9 then

_{S}*T*= 20/9

_{B}04/24/14

Karen K.

04/21/14