Example: If m varies inversely as p, and m = 30 when p = 5, find m when p is 7.
Step 1 Write the equation, “m varies inversely as p”
p
k
m
=⇒
Step 2 m = 30 when p = 5
30
k
=⇒
150
k Use this value of k to solve
the final step
Step 3 find m when p is 6
150
=⇒
m
25
m Done !
With or Against (wind or current)
Once the equation is set up then the next step will require clearing fractions using the LCD. All
solutions must be checked to avoid division by zero.
Use a table to help organize all the information in the problem. Usually only two columns
of the table need to be filled in. The goal is to create the equation using the table.
Example: Garth can row 5 miles per hour in still water. It takes him as long to row 4 miles
upstream as 16 miles downstream. How fast is the current?
The equations for rate (r), distance (d), and time (t) are
d
t
d
rrtd
===⇒ ,,
Let x = speed in still water
Let c = speed of the current
The main difference with these problems is rate needs to be expressed using two variables
because moving upstream the current is against you and downstream it moves with you.
Fill in the distance column with the numbers from the problem above and the value for speed in
still water for x.
c
5
c
5
Fill in the column for time using the other two columns knowing that
time
=⇒