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Polynomials
Distance-Rate-Time
Elimination
Quadratic Formula
Multi-Step Equations
100
-1
constant monomial
100
An aircraft carrier made a trip to Guam and back. The trip there took three hours and the trip back took four hours. It averaged 6 km/h on the return trip. Find the average speed of the trip there.
8 km/h
100
−4x-2y=-12 4x+8y=-24
(6,-6)
100
b^2− 4b+ 4 = 0
{2}
100
9x− 7 = −7
{0}
200
2n^5
quintic monomial
200
A cattle train left Miami and traveled toward New York. 14 hours later a diesel train left traveling at 45 km/h in an effort to catch up to the cattle train. After traveling for four hours the diesel train finally caught up. What was the cattle train's average speed?
10 km/h
200
3x− 2y= 2 5x− 5y= 10
(−2,−4)
200
m^2− 5m− 14 = 0
{7,−2}
200
v/3+ 9/3= 8
{15}
300
9r^6-8
sixth degree binomial
300
Jose left the White House and drove toward the recycling plant at an average speed of 40 km/h. Rob left some time later driving in the same direction at an average speed of 48 km/h. After driving for five hours Rob caught up with Jose. How long did Jose drive before Rob caught up?
6 hours
300
x−y= 11 2x+y= 19
(10,−1)
300
2k^2+ 9k= −7
{−1,−7/2}
300
p− 1 =5p+ 3p− 8
{1}
400
-4 − 2a^2+8a
quadratic trinomial
400
A cargo plane flew to the maintenance facility and back. It took one hour less time to get there than it did to get back. The average speed on the trip there was 220 mph. The average speed on the way back was 200 mph. How many hours did the trip there take?
10 hours
400
3 + 2x−y= 0 −3 − 7y= 10x
(−1,1)
400
k^2− 31 − 2k=−6 − 3k^2− 2k
{5/2,−5/2}
400
24a− 22 =−4(1 − 6a)
No solution.
500
7n^5+10n^4-3n+10n^7
seventh degree polynomial with four terms
500
Kali left school and traveled toward her friend's house at an average speed of 40 km/h. Matt left one hour later and traveled in the opposite direction with an average speed of 50 km/h. Find the number of hours Matt needs to travel before they are 400 km apart.
4 hours
500
2x+ 8y= 6 −5x− 20y= −15
Infinite number of solutions
500
8n^2+ 4n− 16 = −n^2
{−2 +237/9,−2 −237/9}
500
−5(1 − 5x)+5(−8x− 2)=−4x− 8x
{−5}