Rate and Work

Rates and Work For questions in the Quantitative Comparison format (“Quantity A” and “Quantity B” given), the answer choices are always as follows: (A) Quantity A is greater. (B) Quantity B is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given. Where answer choices do not appear on Quantitative Comparison questions in this book, you should choose A, B, C or D based on the above. For questions followed by a numeric entry box | l, you are to enter your own answer in the box. For questions followed by a fraction-style numeric entry box , you are to enter your answer in the form of a fraction. You are not required to reduce fractions. For example, if the answer is —, you may enter or any equivalent fraction. 100 All numbers used are real numbers. All figures are assumed to lie in a plane unless otherwise indicated. Geometric figures are not necessarily drawn to scale. You should assume, however, that lines that appear to be straight are actually straight, points on a line are in the order shown, and all geometric objects are in the relative positions shown. Coordinate systems, such as xy-planes and number lines, as well as graphical data presentations, such as bar charts, circle graphs, and line graphs, are drawn to scale. A symbol that appears more than once in a question has the same meaning throughout the question. 1. Running on a 10-mile loop in the same direction, Sue ran at a constant rate of 8 miles per hour and Rob ran at a constant rate of 6 miles per hour. If they began running at the same point on the loop, how many hours later did Sue complete exactly 1 more lap than Rob? (A) 3 (B) ©) (D) (E) ~N o v B

2. Svetlana ran the first 5 kilometers of a 10-kilometer race at a constant rate of 12 kilometers per hour. If she completed the entire 10-kilometer race in 55 minutes, at what constant rate did she run the last 5 kilometers of the race, in kilometers per hour? (A) 15 B) 12 () 11 (D) 10 (E) 8 3. A standard machine fills paint cans at a rate of 1 gallon every 4 minutes. A deluxe machine fills gallons of paint at twice the rate of a standard machine. How many hours will it take a standard machine and a deluxe machine, working together, to fill 135 gallons of paint? A) 1 B) 1.5 C©) 2 (D) 2.5 (E) 3 4. Wendy can build a birdhouse in 15 hours and Miguel can build an identical birdhouse in 10 hours. How many hours will it take Wendy and Miguel, working together at their respective constant rates, to build a birdhouse? (Assume that they can work on the same birdhouse without changing each other’s work rate.) (A) 5 (B) 6 ©) 7 (D) 8 (E) 9 5. Machine A, which produces 15 golf clubs per hour, fills a production lot in 6 hours. Machine B fills the same production lot in 1.5 hours. How

10. Rajesh traveled from home to school at 30 miles per hour. Then he returned home at 40 miles per hour, and finally he went back to school at 60 miles per hour, all along the same route. What was his average speed for the entire trip, in miles per hour? minutes (A) 32 (B) 36 (C) 40 (D) 45 (E) 47 11. Twelve workers pack boxes at a constant rate of 60 boxes in 9 minutes. How many minutes would it take 27 workers to pack 180 boxes, if all workers pack boxes at the same constant rate? (A) 12 B) 13 (C) 14 D) 15 (E) 16 12. To service a single device in 12 seconds, 700 nanorobots are required, with all nanorobots working at the same constant rate. How many hours would it take for a single nanorobot to service 12 devices? (A) A 3 (B) 28 (C) 108 (D) 1,008 (E) 1,680

13. If a baker made 60 pies in the first 5 hours of his workday, by how many pies per hour did he increase his rate in the last 3 hours of the workday in order to complete 150 pies in the entire 8-hour period? (A) (B) ©) (D) (E) 12 14 16 18 20 14. Nine identical machines, each working at the same constant rate, can stitch 27 jerseys in 4 minutes. How many minutes would it take 4 such machines to stitch 60 jerseys? (A) (B) ©) (D) (E) 3 15. Brenda walked a 12-mile scenic loop in 3 hours. If she then reduced her walking speed by half, how many hours would it take Brenda to walk the same scenic loop two more times? (A) (B) ©) (D) (E) 16. A gang of criminals hijacked a train heading due south. At exactly the same time, a police car located 50 miles north of the train started driving south toward the train on an adjacent roadway parallel to the train track. If the train traveled at a constant rate of 50 miles per hour, and the police car traveled at a constant rate of 80 miles per hour, how long after the hijacking did the police car catch up with the train?

D) 5 (E) 2 20. Phil collects virtual gold in an online computer game and then sells the virtual gold for real dollars. After playing 10 hours a day for 6 days, he collected 540,000 gold pieces. If he immediately sold this virtual gold at a rate of $1 per 1,000 gold pieces, what were his average earnings per hour, in real dollars? (A) $5 B) $6 (C) $7 D) $8 (E) $9 21. After completing a speed training, Alyosha translates Russian literature into English at a rate of 10 more than twice as many words per hour as he was able to translate before the training. If he was previously able to translate 10 words per minute, how many words can he now translate in an hour? (A) 30 (B) 70 (C) 610 (D) 1,210 (E) 1,800 22. Jenny takes 3 hours to sand a picnic table; Laila can do the same job in — hour. Working together at their respective constant rates, Jenny and 2 Laila can sand a picnic table in how many hours? 1 A) — (A) P

(B) 2 9 ©) L 3 (D) 2 7 5 (E) — 6 23. Riders board the Jelly Coaster in groups of 4 every 15 seconds. If there are 200 people in front of Kurt in line, in approximately how many minutes will Kurt board the Jelly Coaster? (A) 5 B) 8 (C) 10 D) 13 (E) 20 A team of 8 chefs produce 3,200 tarts in 5 days. All chefs produce tarts at the same constant rate. Quantity A Quantity B The number of chefs neededto =~ The number of days that 4 chefs 24. produce 3,600 tarts in 3 days need to produce 4,800 tarts 25. Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes. If robot A’s rate of polishing is — that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones?

each day, what is the ratio of the volume of a bottle of Soda Q to a bottle of Soda V? (A) = S (E) E