This week in Pre Calc 11, we learned more about applications of rational expressions, had our unit test, and started reviewing grade 10 Trigonometry. Today I will explain how to do one type of the word problems we had to face this week.
Bronwyn rides her electric bicycle 10km/h faster than Aaron. Bronwyn can travel 60 km in the same time that it takes Aaron to travel 40 km. Determine Bronwyn’s average speed and Aaron’s average speed.
First of all, let Aaron’s speed be x and Bronwyn’s speed be x+10. The other information that we can take from this is the distance. Bronwyn’s being 60 km and Aaron’s being 40 km. These are equal to each other.
To make an equation from this, we can use x and x+10 as the denominators. So, it will look like this:
They are equal to each other because they travel the distances in the same time.
Now, for the numerators, we can put the distances ie: 60 and 40 in there.
So it should look like this:
From here, it is just solving. Since there are only two fractions, we can cross multiply them. This comes out to
60x= 40x +400
Now we just -40x to get
20x= 400
Divide both sides by 20
x=20
Aaron’s average speed is 20 km/h. Bronwyn’s average speed is 30 km/h.
Let’s try another example,
A boat travels 4 km upstream in the same time that it takes the boat to travel 10 km downstream. The average speed of the current is 3 km/h. What is the average speed of the boat in still water?
Let the average speed of the boat in still water be x km per hour. So then the average speed downstream would be (x+3), and the average speed upstream would be (x-3). The distance downstream is 10 km
So, the time downstream is
The average speed upstream is (x-3), and the distance upstream is 4 km.
So, the time upstream is
It takes the same time to travel upstream as it does to travel downstream.
So, an equation is: 
We can cross multiply this equation again. This comes out to
10x – 30 = 4x + 12
Now we can move the 4x to the other side and change the sign
6x – 30 = 12
Move the -30 to the other side and change the sign
6x = 42
Divide both sides by 6
x = 7
So, the average speed of the boat in still water is 7km/h.