Joe's Painting: 20x + 100 = y
Steve's Painting: 15x + 120 = y
x = hours worked
y = total income
We can find when the two equations intersect by making them equal to each other. That means we put an equal sign in the middle. So, it would look something like this:
20x + 100 = 15x + 120
First, we have to move the 100 by subtracting it from both sides.
20x = 15x + 120 - (100)
20x = 15x + 20
Then, we need to move the 15x by subtracting it from both sides.
20 - (15x) = 20
5x = 20
Lastly, we need to divide 5 from both sides.
5x = 20/5
x = 4
Therefore, Joe and Steve would have to work for 4 hours in order for their models to be equal to each other.
One way to solve the system is to <u>substitute</u> a variable.
<u>Explanation:</u>
One approach to solve an equation is by substitution of one variable. Right now, a condition for one factor, at that point substitute that arrangement in the other condition, and explain. All value(s) of the variable(s) that fulfills a condition, disparity, arrangement of conditions, or arrangement of imbalances.
The technique for tackling "by substitution" works by settling one of the conditions (you pick which one) for one of the factors (you pick which one), and afterward stopping this go into the other condition, "subbing" for the picked variable and fathoming for the other. At that point you back-explain for the principal variable.
Answer:
- rate of the boat in still water = 6.5 miles / hour
- rate of the current = 2.5 miles / hour.
Explanation:
<u>1) Name the two variables:</u>
- b: rate of the boat in still water:
With that, the net rates of the boat down the river and upstrean are:
<u>2) Now set the equations for the distance as a function of the times and the rates:</u>
- downstream: 18 miles = (b + c) × 2 hours
- upstream: 18 miles = (b - c) × 4.5 hours
<u>3) Set the system of equations:</u>
- 18 = 2(b + c) ⇒ 9 = b + c . . . Equation (1)
- 18 = 4.5 (b - c) ⇒ 4 = b - c . . . Equation (2)
<u>4) Solve the system by </u><u>elimination</u><u>:</u>
- Add equations (1) and (2): 9 + 4 = 2b
- Divide both sides by 2: 13/2 = b
- Replace b with 6.5 in equation (2) and solve:
4 = 6.5 - c ⇒ c = 6.5 - 4 = 2.5
<u>5) Results:</u>
- b = rate of the boat in still water = 6.5 miles / hour
- c = rate of the current = 2.5 miles / hour.
≈ 0.00020