Answer:
rate of the plane in still air is 33 miles per hour and the rate of the wind is 11 miles per hour
Step-by-step explanation:
We will make a table of the trip there and back using the formula distance = rate x time
d = r x t
there
back
The distance there and back is 264 miles, so we can split that in half and put each half under d:
d = r x t
there 132
back 132
It tells us that the trip there is with the wind and the trip back is against the wind:
d = r x t
there 132 = (r + w)
back 132 = (r - w)
Finally, the trip there took 3 hours and the trip back took 6:
d = r * t
there 132 = (r + w) * 3
back 132 = (r - w) * 6
There's the table. Using the distance formula we have 2 equations that result from that info:
132 = 3(r + w) and 132 = 6(r - w)
We are looking to solve for both r and w. We have 2 equations with 2 unknowns, so we will solve the first equation for r, sub that value for r into the second equation to solve for w:
132 = 3r + 3w and
132 - 3w = 3r so
44 - w = r. Subbing that into the second equation:
132 = 6(44 - w) - 6w and
132 = 264 - 6w - 6w and
-132 = -12w so
w = 11
Subbing w in to solve for r:
132 = 3r + 3(11) and
132 = 3r + 33 so
99 = 3r and
r = 33
Answer:
x=3,y=6
Step-by-step explanation:
2x−y=0
3x−2y=−3
In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
2x−y=0,3x−2y=−3
To make 2x and 3x equal, multiply all terms on each side of the first equation by 3 and all terms on each side of the second by 2.
3×2x+3(−1)y=0,2×3x+2(−2)y=2(−3)
Simplify.
6x−3y=0,6x−4y=−6
Subtract 6x−4y=−6 from 6x−3y=0 by subtracting like terms on each side of the equal sign.
6x−6x−3y+4y=6
Add 6x to −6x. Terms 6x and −6x cancel out, leaving an equation with only one variable that can be solved.
−3y+4y=6
Add −3y to 4y.
y=6
Substitute 6 for y in 3x−2y=−3. Because the resulting equation contains only one variable, you can solve for x directly.
3x−2×6=−3
Multiply −2 times 6.
3x−12=−3
Add 12 to both sides of the equation.
3x=9
Divide both sides by 3.
x=3
The system is now solved.
x=3,y=6
Answer:
e
Step-by-step explanation:
Answer:$90
Step-by-step explanation: 5x15=75
5x3=15+75=90