In many, many cases, the "known relationship" is expressed as a mathematical equation. The relationship between the rate something happens and the amount of something produced is very common, so this discussion will use a couple of rate problems as its example.
In most general terms, the amount of something produced is equal to the rate of production times the amount of time production took place. For instance, in a displacement problem, rate is how far something moves in a given time and motion of an object is produced. In a general form a rate problem might look like this:
O = R•t
where O is the output, R is the rate, and t is the time.
So what is this process of solving science problem that will use rate problems as its example?
There are three steps to solving ANY science problem (or word problem of any kind, for that matter).
The following two examples will be used as the steps are discussed:
EXAMPLE 1: A baker's oven will hold only 1 pan of cookies, and each pain has space for 12 cookies. The baking time on cookies (including putting the dough on the pan) is 20 minutes. Therefore, the rate cookies are baked is 12 cookies per 20 minutes. How many cookies can be baked in 80 minutes?
EXAMPLE 2: A car travels at an average rate of 20 MPH for 3 hours. How far does it go.
The first step is to write down what is given and what is asked.
R = 12 cookies/20minutesExample 2:
t = 80 minutes
LOOKING FOR "How many cookies"
R= 20 MPH
LOOKING FOR "How far does it go"
A student familiar with physics motion problems would see Example 2 as a "distance" problem and would use the distance equation variables. In such a case, R would be velocity, v, t would be time, t, and LOOKING FOR would be distance, d (or in some cases, s).The second step is to write the equation that relates to the question.
Cookies = R•t
d = vtThe third step is to plug in what was given and solve. Assuming the second step was completed, the following solutions would emerge:
Cookies = R•t
Cookies = 12 Cookie/20 min • 80 min
Cookies = 960 Cookie•min / 20 min
Cookies = 48 Cookie
d = vt
d = 20 mi/hr * 3hr
d = 60 (mi•hr)/hr
d = 60 mi
There are three steps to solving problems.
1: Write down what is given.
2: Write down the relevant equation.
3. Plug in and solve.