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Cards In This Set
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Two trains running in the same direction on the same track travel at the rates of 40 and 45 mph, respectively. If the slower train starts out an hour earlier, how long will it take the faster train to catch up with it?
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The slower train is 40 miles ahead in one hour. The difference in rate is 5 mph, and
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A naval detachment has enough rations to feed fifteen people for 8 days. If five more people join the detachment, for how many fewer days will the rations last?
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Let x = the number of ration days for 20 persons.
 Therefore 8 days – 6 days = 2 days fewer. |
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A field can be plowed by 12 machines in 7 hours. If 4 machines are broken and cannot be used, how many hours will it take to plow the field?
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Let x equal the number of hours to plow with 8 machines. So,
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What is the square root of 4 raised to the fifth power?
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If 3n – 2 = 27, what does n equal?
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If the sum of the edges of a cube is 24 inches, what is the volume of the cube?
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A cube has 12 edges, so each edge is
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How much pure acid must be added to 10 ounces of a 55% acid solution in order to produce a 75% acid solution?
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ounces parts pure acid no. of ounces of pure acidpure acid x 100 100x40% acid solution 10 55 55060% acid solution 10 + x 75 75(10 + x)
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A farmer who is 6 feet tall wants to determine the height of his barn. He notices that his shadow is 14 feet long and that his barn casts a shadow 70 feet long. How high is the barn?
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If (x – y)2 = 60 and x2 + y2 = 40, then xy =
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In the figure shown below, what is the measure of angle x?
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Arc AB = 80° therefore, AOB = 80°. The two radii are equal.
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Jane received grades of 93, 82, and 72 on three tests. What grade must she receive on the next test so that her average for these four tests is 85?
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Jane's current test grades total 247: 93 + 82 + 72 = 247. To average 85, Jane's grades must total 340: 85 × 4 = 340. To raise her average grade, Jane must earn 93 on the next test: 340 – 247 = 93.
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A family drove from New York to San Francisco, a distance of 3,000 miles. They drove
 of the distance the first day and  of the remaining distance the second day. How many miles were left to be driven? |
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In a 4–hour examination of 420 questions, there are 60 mathematics problems. If twice as much time should be allowed for each mathematics problem as for each of the other questions, how many minutes should be spent on the mathematics problems?
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Let x = minutes to be spent on each math problem.
 So, 60x = 60 minutes to be spent on the 60 math problems. |
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1,000,000 may be represented as
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10 × 10 × 10 × 10 × 10 × 10 = 1,000,000, or 10 raised to the 6th power.
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If a = 4b and 8b = 30c, then a =
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a = 4b
2a = 8b = 30c 2a = 30c a = 15c. |
