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Cracking the SAT Subject Test in Math 2, 2nd Edition (C) 83 23 (D) 64 00 (E) 53 83 26 If the square of x varies inversely with the cube root of the square of y, and y = 8 when x = , then what is the v[.]
(C) 83.23 (D) 64.00 (E) 53.83 26 If the square of x varies inversely with the cube root of the square of y, and y = 8 when x = , then what is the value of x when y = ? (A) 0.630 (B) (C) 1.587 (D) 1.260 (E) 39 If the cube root of the sum of x and 2 varies inversely with the square of y, and x = 6 when y = 3, then what is the value of x when y = 6? (A) −1.875 (B) 0.125 (C) 0.5 (D) (E) 18 WORK AND TRAVEL QUESTIONS Word problems dealing with work and travel tend to cause a lot of careless mistakes, because the relationships among distance, time, and speed—or among work-rate, work, and time—sometimes confuse test takers When working with questions about travel, just remember this: distance = rate × time When working with questions about work being done, remember this: work done = rate of work × time Look Familiar? If these two formulas seem the same, it’s because they are After all, what is work done if not the distance from the start of work to the end? Don’t worry about learning too many equations; generally speaking, the few you’ll need are more useful than their wording indicates DRILL 9: WORK AND TRAVEL QUESTIONS Answer the following practice questions using these formulas The answers can be found in Part IV A factory contains a series of water tanks, all of the same size If Pump 1 can fill 12 of these tanks in a 12-hour shift, and Pump 2 can fill 11 tanks in the same time, then how many tanks can the two pumps fill, working together, in 1 hour? (A) 0.13 (B) 0.35 (C) 1.92 (D) 2.88 (E) 3.33 A projectile travels 227 feet in one second If there are 5,280 feet in 1 mile, then which of the following best approximates the projectile’s speed in miles per hour? (A) 155 (B) 170 (C) 194 (D) 252 (E) 333 A train travels from Langston to Hughesville and back in 5.5 hours If the two towns are 200 miles apart, what is the average speed of the train in miles per hour? (A) 36.36 (B) 72.73 (C) 109.09 (D) 110.10 (E) 120.21 10 Jules can make m muffins in s minutes Alice can make n muffins in t minutes Which of the following gives the number of muffins that Jules and Alice can make together in 30 minutes? (A) (B) (C) 30(mt + ns) (D) (E) 28 Samantha is running a race that is x meters She runs the first 40% of the race at y meters per second and the remainder of the race at z meters per second How long, in seconds, does it take for Samantha to finish the race? (A) (B) (C) x(0.4y+0.6z) (D) 0.24xyz (E) Average Speed The “average speed” question is a specialized breed of travel question Here’s what a basic “average speed” question might look like Roberto travels from his home to the beach, driving at 30 miles per hour He returns along the same route at 50 miles per hour If the distance from Roberto’s house to the beach is 10 miles, then what is Roberto’s average speed for the round-trip in miles per hour? (A) 32.5 (B) 37.5 (C) 40.0 (D) 42.5 (E) 45.0 The easy mistake to make on this question is to simply choose (C), the average of the two speeds Average speed isn’t found by averaging speeds, however Instead, you have to use this formula: Won’t Get Fooled Again If an answer choice looks too good to be true, it probably is Finding the average of two averages is more than just averaging the two together, but knowing this allows you to eliminate (C), as it is a trap answer The total distance is easy to figure out—10 miles each way is a total of 20 miles Total time is a little trickier For that, you have to use the “distance = rate × time” formula Here, it’s useful to rearrange the eqution to read as follows: On the way to the beach, Roberto traveled 10 miles at 30 mph, which took 0.333 hours, according to the formula On the way home, he traveled 10 miles at 50 mph, which took 0.2 hours That makes 20 miles in a total of 533 hours Plug those numbers into the average-speed formula, and you get an average speed of 37.5 mph The answer is (B) Here’s a general tip for “average speed” questions: On any round-trip in which the traveler moves at one speed heading out and another speed returning, the traveler’s average speed will be a little lower than the average of the two speeds Look Familiar? This formula may look familiar to you That’s because it’s taken from our Average Pie Another way to work with average speed questions is to use the Average Pie where the total is the total distance and the number of things is the time So it would look like this: DRILL 10: AVERAGE SPEED Try these “average speed” questions The answers can be found in Part IV Alexandra jogs from her house to the lake at 12 miles per hour and jogs back by the same route at 9 miles per hour If the path from her house to the lake is 6 miles long, what is her average speed in miles per hour for the round-trip? (A) 11.3 (B) 11.0 (C) 10.5 (D) 10.3 (E) 10.1 11 A truck travels 50 miles from Town S to Town T in 50 minutes, and then immediately drives 40 miles from Town T to Town U in 40 minutes What is the truck’s average speed in miles per hour, from Town S to Town U ? ... Jules can make m muffins in s minutes Alice can make n muffins in t minutes Which of the following gives the number of muffins that Jules and Alice can make together in 30 minutes? (A) (B) (C) 30(mt + ns)... Answer the following practice questions using these formulas The answers can be found in Part IV A factory contains a series of water tanks, all of the same size If Pump 1 can fill 12 of these tanks in a 12-hour... A projectile travels 227 feet in one second If there are 5,280 feet in 1 mile, then which of the following best approximates the projectile’s speed in miles per hour? (A) 155 (B) 170 (C) 194 (D) 252 (E) 333 A train travels from Langston to Hughesville and back in