Solving Rate Problems: Quiz
Working together, Katherine and Marina can sand a large cabinet in 2 hours. It would take Katherine 10 hours to do the job alone. What is the value of r, the part of the job that Marina can complete in 1 hour?
B. 0.4
Sophie and Simon are peeling a pile of potatoes for lunch in the cafeteria. Sophie can peel all the potatoes by herself in 45 minutes, while it would take Simon 30 minutes to do the job working alone. If Sophie and Simon work together to peel the potatoes, how long will it take them?
B. 18 minutes
Working together, Alex and Millie can file all the papers in the file cabinets in 4 hours. It would have taken Alex 6 hours to do the job alone. What is the missing value in the table that represents the part of the papers that Alex would file if Alex and Millie worked together?
B. 4/6
Milla and Luka are 3 kilometers apart and walking toward each other. Milla's average speed is 5 kilometers per hour and Luka's is 4 kilometers per hour. Which equation can be used to find t, the time it takes for Milla and Luka to meet?
B. 5t+4t=3
It would take Marco 6 hours to paint a fence by himself. It would take Jaylyn 5 hours to paint the same fence by herself. Marco is creating this table to help him determine how long it would take them to paint the fence together. Which heading should be written above the first column of numbers?
A. Rate (part/hour)
Eduardo's average speed on his commute to work was 55 miles per hour. On the way home, he hit traffic and only averaged 40 miles per hour. If the round trip took him 1.25 hours, which expression represents the distance, in miles, for his trip home that is missing from the table?
C. 40(1.25 - t)
Yuto and Lian are at train stations 1,880 kilometers apart. Yuto boards a train heading east at an average speed of 220 kilometers per hour. At the same time, Lian boards a train heading west on a parallel track at an average speed of 250 kilometers per hour. How far has Lian traveled when the two trains pass each other?
D. 1,000 kilometers
Mike and Jamal are 9 miles apart, and are planning to meet up. Mike is walking at an average speed of 3 miles per hour to meet Jamal. Jamal is driving at an average speed of 25 miles per hour to meet Mike.Which equation can be used to find t, the time it takes for Mike and Jamal to meet?
D. 25t + 3t = 9
The average rate of the first part of Yi's walk on a park loop was 4 miles per hour. She then met up with a friend and the two walked the rest of the way at an average rate of 5 miles per hour. The entire 3-mile walk took Yi 42 minutes (0.7 hour). Which equation can be used to solve for x, the time in hours that Yi spent walking before meeting her friend?
D. 4x + 5(0.7 - x) = 3
Craig ran the first part of a race with an average speed of 8 miles per hour and biked the second part of a race with an average speed of 20 miles per hour. The entire two-part, 15-mile race took him 1.125 hours to complete. Which table correctly represents his rates, times, and distances for each part of the race?
Table One