Solving Quadratics (ZPP, CTS, QF, SR)
x2 - 5x - 14 = 0
(x - 7)(x +2) = 0
x ε {7,-2}
r + sy = t
solve for y
t - r/s = y
Jack can pack 2 more lunches per minute than Chris. Chris packs lunches for 15 minutes, and Jack joined him for all but 2 of those minutes. Write an expression for the total number of lunches they pack.
Let x = the amount of lunches Chris packs
15x+ (2+x) (13)
15x+26 + 13x
28x + 26 lunches
Pedro can bike twice as fast as he can run. One day he biked 10 miles to his grandmother’s house, and he ran back. The entire trip took 2.5 hours. How fast did Pedro run?
6 mph
y = 2x
y = -16
(x, y) (-8,-16)
4x4-5x2-9 = 0
x ε {-3/2, 3/2}
od - x = ud + y (solve for d)
d = x +y/o - u
A ship left a port at 3:00 PM and sailed east at 30 mph. Another ship left the port at 3:40 PM and sailed the same way at 54 mph. When did it catch up to the first one?
30x = 54x -36
36=24x
x= 3/2
4:30 PM
Timmy can fill his wading pool with water from the garden hose in 45 minutes. Timmy’s big brother can pump water from the well and fill the pool in 30 minutes. How long would it take to fill the pool using both the garden hose and the pump?
18 minutes
2x + 3y = 8
6x + 5y = 0
(x,y) = (-5,6)
-2x2 - 5x + 13 = 0
x = (-5 +- √129)/4
9y - 24a = 6a + 4y
solve for y
y = 6a
Jane rode her bike for 5 miles. She then drove her car for the same distance at a rate 10 times as fast as she rode her bike. If the entire journey took 2 hours, how fast did she ride her bike?
let x =rate of bike
5/x + 5/10x = 2
multiply by 10x
50 + 5 =20x
x= 11/4
2 3/4 mph
Ethel Lete runs 12 miles and then walks 16 more miles. She can run twice as fast as she can walk. The total elapsed time is 5 hours. How fast does Ethel walk?
4.4 mph
4x + 3y = 6
8x + 6y = -6
(x,y) ε {}
x3 +729 = 0
X=-9
-2y + 12 = |x + 1|
Check Google Doc
It takes Fiona 3 days to paint a certain house. David could paint the same house in 4 days. How long would it take them to paint the house if David and Fiona work together?
let x= time spent
rate of 1/4 and 1/3
x(1/4 + 1/3) =1
3x + 4x =12
x = 12/7
5/7 days
Chuck can shovel the snow off his driveway in 40 minutes. He shovels for 20 minutes and then is joined by Joan. If they shoved the remaining snow in 10 minutes, how long would it have taken Joan to shovel the driveway alone?
40 minutes
g + m + p = 10
2g = m
3p + 4m + 5g = 72
g = 3
m = 6
p =11
2x2 -6x - 2 = 0
x ε { (3 ± √13)/2 }
y = 2|x-4| + 3
Check Google Doc
Katya can fold 18 programs per minute. James can fold 20 programs per minute. Katya started folding programs at 2:30 PM, and James started 4 minutes later. They stopped when they had folded 338 programs. At what time did they stop?
x= minutes worked
18x + 20 (x-4) = 338
18x+20x= 418
38x=418
x=11
2:41 PM
Three pipes are connected to a water tank. One of the pipes can fill the tank in 30 minutes. The second pipe can fill it in 20 minutes. The third pipe can fill the tank in 40 minutes. If the slowest pipe is shut off after 3 minutes and the fastest pipe is shut off 3 minutes later, how long will it take the remaining open pipe to finish filling the tank?
12 minutes 45 seconds
c + g +x = 50
-2c - 1 = -g
40x + 30g + 50x = 1880
c = 12
g =25
x= 13