Week 14 – Precalc 11 – Caleb’s Blog

Word problems involving Rational Expressions was the final lesson before the Unit Test on week 14. Inserting the information given in a word problem into a rational expression was a struggle at first but once I understood the concept, the numbers fell into its correct place. These rational equations can be applied to real-world problems involving motion, work, and proportions. Question 6 (on Page 596) is a perfect example of work.

6) Jenny can clean out the garage in 5h. When her son helps, they can clean out the garage in 3h. How long would it take Jenny’s son to clean out the garage on his own?
First of all, a table is created to organize the information and let $x$ represent the unknown variable.
Let $x$ represent the time for Jenny’s son to clean out the garage on his own.

Now, the organized information can be converted into a rational equation.

Time	Jenny	Jenny’s Son	Jenny & Son
Own Time	5	$x$	3
1	$\frac{1}{5}$	$\frac{1}{x}$	$\frac{1}{3}$
3	$\frac{3}{5}$	$\frac{3}{x}$	$\frac{3}{3}$ = 1

Now, the organized information can be converted into a rational equation.

Find the common denominator and solve for $x$ .

It would take Jenny’s son 7.5 hours ( $\frac{15}{2}$ hours) to clean the garage on his own.

Question 7 (on Page 597) is a word problem involving proportion.
7) How much bleach should be added to 47L of water to make a solution that is 6% bleach?
Let $x$ represent the amount of bleach added.
A rational equation can be created using the information.

Now, find the common denominator and solve for $x$ .

3 litres of bleach should be added.

This last question involves motion and the concept of Speed, Distance, and Time.
8) A boat travels 4km upstream in the same time that it takes the boat to travel 10km downstream. The average speed of the current is 3km/h. What is the average speed of the boat in still water?
Let $x$ represent the average speed of the boat in still water.

	Upstream	Downstream
Distance (km)	4	10
Speed	$x - 3$ (against the current)	$x + 3$ (with the current)
3	$\frac{4}{x - 3}$	$\frac{10}{x + 3}$

Now, the organized information can be converted into a rational equation.

Now, find the common denominator and solve for $x$ .

The average speed of the boat in still water is 7 km/h.

Week 14 – Precalc 11

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