Unit 4: Rational Expressions & Equations Assignment

1. Eva and Wilson are watching a Netflix movie at home. By himself, Wilson can eat a whole bag of popcorn in 20 minutes. Eva takes 30 minutes to eat a whole bag of popcorn. If they both eat popcorn at their usual rates, how long will it take Eva and Wilson to finish a single bag of popcorn if they share? (2 marks)

2. The quotient of 36 and a whole number increased by 3, is 20 less than four times the number. Find the number(s). (2 marks)

7. In June 2020, Parks Canada closed the Bow Valley Parkway (Highway 1A) to vehicle traffic between Banff and Castle Junction near Johnston Canyon. This made for a bike ride that cut through a small piece of Canada's beautiful Rocky Mountains. A group of friends decide to cycle the trip, 25 km each way, from Banff to Johnston Canyon and back. They ride towards Johnston Canyon straight into the wind, and then have the wind at their backs on the return trip. The wind adds or subtracts 5 km/h from their speed. If the group of friends wants to complete the round trip in 3 hours, algebraically find the average speed with no wind the group needs to cycle. Complete the distance speed time chart to help solve the question. Round your answer to the nearest hundredth of a km/h. (3 marks) Distance Speed Time Banff to Johnston Canyon Johnston Canyon to Banff8. In Math 20-1 class, the teacher gives the class the following rational expressions. 7x2 42x x2 2x35 xZx30 x249 a. State all non-permissible values of x in the expressions above. (1 mark) b. Determine the simplied product of the two expressions above. (1 mark) c. The Math 20-1 teacher also gives the class a diagram of a rectangle with dimensions represented by rational expressions, where x > 2 , as shown below. Explain why x > 2 for the rectangle. (1 mark) d. The teacher reminds the class that the perimeter of a rectangle is the sum of the lengths of all the sides. Given that the perimeter of the given rectangle is 60 cm , write an equation that can be used to solve for x. Algebraically determine the value of x, to the nearest tenth, using this equation. (2 marks) -2 5 4. Explain two ways to solve =2+- graphically. Draw a sketch of each method. State the x+3 X solution(s) to the equation. Round your answer(s) to the nearest tenth if necessary. (5 marks) #+ + H H