Question 1: A runner runs at a constant speed and covers a certain distance in 30 minutes. The distance is modeled by the equation d = 5x, where x is the speed in km/h. Another athlete's quadratic distance traveled after x hours is given by D = 4x^2 + 2x. Find the speed at which both athletes run the same distance.

Answer: 6

Question 2: Solve for x: 3x + 2 = x^2 - 4.

Answer: x= -1 or x= 5

Question 3: A cyclist's linear distance covered is given by d = 10x, where x is hours. A different route's quadratic distance after x hours is D = x^2 + 8x. Find the time when both distances are equal.

Answer: 2

Question 4: If a basketball player scores points modeled by y = 2x + 3 and the quadratic model for another player's points is y = x^2 + x, find when they score the same number of points.

Answer: x=1

Question 5: A swimmer's linear distance after x hours is D = 6x. A different swimmer's quadratic distance is D = 2x^2 + 4x. Determine the time when their distances are equal.

Answer: 3

Question 6: Solve the system: 2x + y = 10 and y = x^2 - 4.

Answer: x=2 or x=-1, y=6 or y=-5

Question 7: In a fitness challenge, the linear relation between steps walked and days is given by S = 100x. The quadratic relation for another activity is S = x^2 + 50x. When do both activities result in the same number of steps?

Answer: 4

Question 8: A sprinter's distance as a function of time is given by d = 3x + 5. Another athlete's quadratic distance is d = x^2 + 2x + 1. Find the time when their distances are equal.

Answer: 1

Question 9: A football player's goals over x matches follow y = 2x + 4. Another player's goals follow y = x^2 + 3x. Determine the number of matches after which both players have scored the same number of goals.

Answer: 2

Question 10: Error Analysis: A student solves the system: x + y = 5 and y = x^2 - 1, claiming the solutions are x=2 and y=3. Identify the mistake and correct the solution.

Answer: Student incorrectly substituted x=2 into y=x^2 -1, which gives y=3, but the first equation gives y=5 - x. Correct solution: x=2, y=3 does not satisfy x + y=5; actual solutions are x=2, y=3 (which does satisfy the first). The mistake is in the initial assumption; the actual solutions are x=2, y=3.