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Mary can make 20 snowballs in an hour. Mark can make 15 snowballs in 30 minutes. If they work together, how long will it take them to make 150 snowballs?
If Mark makes 15 snowballs in 30 minutes, he can make 30 snowballs in an hour. Working together they can 50 snowballs in one hour. 150 snowballs divided by the amount they can make in one hour (50) will give us the total time it will take them to make 150 snowballs. In this case, 3 hours.
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Car X used 4 gallons of gas in one week, and gets 10 miles to the gallon. If car Y went the same number of miles but only gets 8 miles to the gallon, how much gas did car Y use?
We first use the data for car X to conclude that car X went 40 miles (4gallons*10mi/gallon). We then use 40 miles for car Y, and divide 40 by 8, to give us 5 gallons of gas.
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Susan is doing a bake sale for her sorority. One third of the money she made is from blueberry cupcakes, which cost 50 cents each. A quarter of her sales is from cinnamon cream pies, which cost $1 each. And the rest are from her chocolate brownies, which cost 25 cents each. She made a total of $60 at the end of her bake sale, how many brownies did she sell?
1/3 of sales from cupcakes = $20, ¼ of sales from cream pies = $15 and the rest are from brownies = $60-$20-$15 = $25. Since each brownie costs 25 cents, Susan will have sold 100 of them.
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Bob and Sally are doing chores. It takes them 10 hours to do one of their chores. Assuming everyone works at the same rate, how many of their friends would they need to get to help them to do their chores in 2 hours?
Since the kids are trying to do their chores in one fifth of the time, they need five times as many people. Since they have two, five times as many would be ten. We subtract the two of them and that would mean they need 8 more people, giving us answer 8.
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A water tank holds 500 gallons of water. There is a hole in the tank that leaks out the water at rate of 100 mL/min. In how many days will the water tank contain only half of the water it holds originally? Note: 1 gallon = 3.785 L
1 gallon = 3.785L = 3785mL, half of the tank = 250*3785 = 946,250mL. To find the minutes, 946250mL/(100mL/min) = 9462.5min. Since 1 day=24hr*60min=1440min, the number of days =94625min/(1440min/day)=6.5 days
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Alex runs around his school race track one time in 15 minutes and takes another 25 minutes to run around a second time. If the course is 4 miles long, what is his approximate average speed in miles per hour for the entire run?
15 + 25 = 40 minutes. 40 minutes is 2/3 of an hour. Distance = rate x time. Using this formula, we have 4 = (2/3) r. To solve for r we multiply both sides by (2/3). r = 6
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If a car travels 60 mph for 2 hours, 55 mph for 1.5 hours and 30 mph for 45 minutes, how far has the car traveled?
Distance traveled = mph x hour
60mph x 2hours + 55mph x 1.5 hours + 30 mph x 45 minutes (or .75 hours) =
120 miles + 82.5 miles + 22.5 miles = 225 miles
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If an object travels at 1200 ft per hour, how many minutes does it take to travel 180 ft?
1200 ft per hour becomes 20 ft per second (divide 1200 by 60 because there are 60 minutes in an hour). 180/20 is 9, giving 9 minutes to travel 180 ft.
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If you live 3 miles from your school. What average speed do you have to ride your bike get to your school from your house in 15 minutes?
The best way to find speed is to divide the distance by time. Since time is given in minutes we must convert minutes to hours so that our units match those in the answer choices. (3miles/15min)(60min/1hr)=12miles/hr; Remember when multipliying fractions to multiply straight across the top and bottom.
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In 7 years Bill will be twice Amy’s age. Amy was 1.5 times Molly’s age 2 years ago. If Bill is 29 how old is Molly?
Consider
(Bill + 7) = 2 x (Amy + 7)
(Amy – 2) = 1.5 x (Molly – 2)
Solve for Molly using the two equations by finding Amy’s age in terms of Molly’s age.
Amy = 2 + 1.5 Molly – 3 = 1.5 x Molly – 1
Substitute this into the first equation:
(Bill + 7) = 2 x (Amy + 7) = 2 x (1.5 x Molly – 1 + 7) = 2 x (1.5 x Molly + 6) = 3 x Molly + 12
Solve for Molly:
Bill + 7 – 12 = 3 x Molly
Molly = (Bill – 5) ¸ 3
Substitute Bill = 29
Molly = (Bill – 5) ¸ 3 = 8
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If an airplane is flying 225mph about how long will it take the plane to go 600 miles?
Speed = distance /time; So by solving for time we get time = distance /speed. So the equation for the answer is (600 miles)/ (225 miles/hr)= 2.67 hours; Remember to round up when the last digit of concern is 5 or more.
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In a mixture of flour and sugar, the ratio of flour to sugar is 5 to 1. How many kilograms of flour will there be in 12 kilograms of this mixture?
The question says that the mixture has 5 units of flour for every 1 unit of sugar, which adds up to a total of 5 + 1 = 6 units of the mixture; therefore in 6 kilograms of the mixture, 1 kilogram will be sugar.
To find how much sugar will be in 12 kilograms of the mixture, we multiply the amount of sugar in 6 kilograms of the mixture by 2, giving us 1 kilogram of sugar * 2 = 2 kilograms of sugar.
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A survey of studio offices in a city with 14,000 employees reveals that there are, on average, 12.5 employees per office. If there have been a cumulative total of 3,400 printers sold to the offices of the city, what is the best estimate of the average number of printers per office?
The best estimate would be to simply divide the number of printers by the number of offices. However, they only gave us the average number of employees per office, thus to find the number of offices we divide:
14,000 (people)/12.5 (per office) = 14,000/12.5 = 1,120 offices
We already know the number of printers available total, thus again divide
3,400 (printers)/1,120 (offices) = 3.04, or 3.0 printers per office as the best estimate.
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A factory makes six widgets in a batch that takes 24 minutes to complete. How long does it take to make 57 widgets?
We have here a basic ratio:
6/24 = 57/x
Solving for x, we get: 6x = 24 * 57; 6x = 1368; x = 228
Now, we must be very careful here, however. Is 228 an even multiple of 24? 228/24 = 9.5. That means that we would have to do 9.5 batches. The question indicates that these are batched in groups of 6; therefore, we have to run 10 batches to get our amount. That would be 240 minutes or 4 hours.
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If the ratio of q to r is 3:5 and the ratio of r to s is 10:7, what is the ratio of q to s?
Multiply the ratios. (q/r)(r/s)= q/s. (3/5) * (10/7)= 6:7.
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The first term in a sequence is m. If every term thereafter is 5 greater than 1/10 of the preceding term, and m≠0, what is the ratio of the second term to the first term?
The first term is m, so the second term is m/10+5 or (m+50)/10. When we take the ratio of the second term to the first term, we get (((m+50)/10))/m, which is ((m+50)/10)(1/m), or (m+50)/10m.
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Two cars were traveling 630 miles. Car A traveled an average speed of 70 miles per hour. If car B traveled 90 miles an hour, how many miles had car A traveled when car B arrived at the destination?
We first divide 630 miles by 90 miles per hour to get the amount of time it took car B to reach the destination, giving us 7 hours. We then multiply 7 hours by car A’s average speed and we get 490 miles.
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| STUDENT ATHLETES WHO USE STEROIDS | |||
|---|---|---|---|
| MEN | WOMEN | TOTAL | |
| BASKETBALL | A | B | C |
| SOCCER | D | E | F |
| TOTAL | G | H | I |
In the table above, each letter represents the number of students in each category. Which of the following must be equal to I?
Since G is the total number of male athletes that use steroids and H is the total number of female athletes that use steroids, the sum of the two is equal to I, which is the total number of all students using steroids.
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A particular ball always bounces back to 2/5 of the height of its previous bounce after being dropped. After the first bounce it reaches a height of 175 inches. Approximately how high (in inches) will it reach after its fifth bounce?
The first bounce reaches a height of 175. The second bounce will equal 175 multiplied by 2/5 or 70. Repeat this process. You will get the data below. 4.48 is rounded to 4.5.
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A mile is 5280 feet
Susan is able to walk a fast pace of 4 miles per hour. How many feet will she walk in 40 minutes?
Calculate the number of feet walked in an hour. Then calculate what fraction of an hour 40 minutes is.
5280 * 4 = 21120 feet walked in an hour
60 minutes in an hour, so 40 minutes = 2/3 hour (40/60)
21120(2/3) = 14080 feet walked in 40 minutes
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