SAT Math : Proportion / Ratio / Rate
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Example Questions
Example Question #21 : Arithmetic
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?
185 minutes
120 minutes
2.5 hours
3 hours
3 hours
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.
Example Question #2 : How To Find Rate
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?
5 gallons
8 gallons
10 gallons
4 gallons
5 gallons
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.
Example Question #1 : How To Find Rate
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?
10
8
None of the above
5
8
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.
Example Question #22 : Arithmetic
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
7.5
8
6
6.5
7
6.5
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
Example Question #11 : How To Find Rate
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?
10
6
4
8
6
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
Example Question #31 : Proportion / Ratio / Rate
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?
225 miles
145 miles
1552.5 miles
120 miles
202.5 miles
225 miles
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
Example Question #33 : Proportion / Ratio / Rate
If an object travels at 1200 ft per hour, how many minutes does it take to travel 180 ft?
7 minutes
11 minutes
10 minutes
9 minutes
8 minutes
9 minutes
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.
Example Question #34 : Proportion / Ratio / Rate
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?
3 miles/hour
12 miles/hour
15 miles/hour
10 miles/ hour
5 miles/hour
12 miles/hour
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.
Example Question #1591 : Psat Mathematics
If an airplane is flying 225mph about how long will it take the plane to go 600 miles?
2.5 hours
2.4 hours
3.2 hours
2.7 hours
3.5 hours
2.7 hours
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.
Example Question #12 : How To Find Rate
Vikki is able to complete 4 SAT reading questions in 6 minutes. At this rate, how many questions can she answer in 3 1/2 hours?
170
210
150
35
140
140
First, find how many minutes are in 3 1/2 hours: 3 * 60 + 30 = 210 minutes. Then divide 210 by 6 to find how many six-minute intervals are in 210 minutes: 210/6 = 35. Since Vikki can complete 4 questions every 6 minutes, and there are 35 six-minute intervals we can multiply 4 by 35 to determine the total number of questions that she can complete.
4 * 35 = 140 problems.
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