Download Applications of Rational Equations

Applications of Rational Equations
Shoveling Snow
After a heavy snowfall, Brian can shovel all of the driveway in 30 minutes. If his younger
brother Allen helps, the job takes only 20 minutes. How long would it take Allen to do
the job by himself?
To solve the problem, answer each of the questions:
1. If it takes Brian 30 minutes to shovel the entire driveway, which fraction of the
driveway would be shoveled in 20 minutes?
Brian shovels
of driveway in 20 minutes. (1)
2. Let x be the number of minutes it would take Allen to shovel the entire driveway
by himself. Which fraction of the driveway (in terms of x) would Allen shovel in
20 minutes?
Allen shovels
of driveway in 20 minutes. (2)
3. When Allen helps Brian to shovel all of the driveway, the sum of Brian’s fraction
(1) and Allen’s fraction (2) equals 1. In other terms, we have:
+
=1
(3)
4. Solve equation (3) to find x
x = _______
Mixing water and antifreeze
How much pure antifreeze liquid should be added to 1 gallon of a 40% antifreeze
solution to get a 60% antifreeze concentration?
Note. There is 0.4 gallons of pure antifreeze in 1 gallon of 40% antifreeze solution.
To solve the problem, answer each of the questions:
1. We add x gallons of pure antifreeze to 1 gallon of 40% antifreeze solution.
The total volume of pure antifreeze in the new solution is
______ + _____ = _____________ gallons (1)
The total volume of liquid in the new solution is
______ + _____ = _____________ gallons
(2)
2. To satisfy the volume of 60% concentration, we divide the amount found in (1) by
the amount found in (2) and we obtain the equation
" (1)"
(3)
 0.6
" (2)"
3. Solve equation (3) to find x.
x = _________