All SAT Math Resources
Example Questions
Example Question #21 : How To Find Rate
Two brothers, Jake and Fred, have a pool in which 9 laps is 1 mile. Jake swims 2 laps in 1 minute, and Fred swims 4 laps in 1 minute. How far has Jake swum when Fred has finished swimming 2 miles?
3/2 miles
1 mile
9/2 miles
2 miles
3/4 miles
1 mile
We can solve this with lots of calculations and conversions of laps to miles, etc., or we can look at what the question is really asking. We want to know how far Jake swims in the time it takes Fred to swim two miles. Instead of converting Fred's miles to laps and comparing to Jake's laps, let's just look at how fast the two brothers swim in relation to one another. Fred swims twice as fast as Jake, so in the same amount of time, he will swim twice as far as Jake. Therefore if Fred swims 2 miles, Jake swims 1 mile in the same amount of time.
Example Question #41 : Proportion / Ratio / Rate
Every 3 minutes, 4 liters of water are poured into a 2,000-liter tank. After 4 hours, what percent of the tank is full?
60 minutes in an hour, 240 minutes in four hours. If 4 liters are poured every 3 minutes, then 4 liters are poured 80 times. That comes out to 320 liters. The tank holds 2,000 liters, so of the tank is full.
Example Question #41 : Proportion / Ratio / Rate
Example Question #51 : Proportion / Ratio / Rate
Laura owns a large property. Her lawn is rectangular. It is 500 meters long, and 350 meters wide. If Laura mows the lawn at a rate of 20,000 meters squared per hour, how many hours will it take Laura to finish mowing the lawn?
The area of a rectangle is the length , multiplied by the width . Here the area of the lawn in meters squared is:
We found that Laura is mowing 175,000 meters squared at a rate of 20,000 meters squared per hour.
Plugging in 20,000 for the rate, and 175,000 for the total area gives:
Multiply both sides by the total number of hours:
Now, divide both sides by 20,000:
Example Question #27 : How To Find Rate
Jess is trying to fill her 10,000 gallon pool with water before the summer. She has three hoses, one that pump water at a rate of 175 gallons per hour, 25 gallons per hour and 200 gallons per hour. If she used all three hoses how many hours would it take to fill her pool?
First add up all of the rates to get the total rate of water flowing into the pool at one time.
Then to determine the time it takes to fill the pool divide the total volume of the pool by this rate.
This answer of 25 hours.
Example Question #53 : Proportion / Ratio / Rate
Joaquin can clean a pool in j minutes. River can clean the same size pool in r minutes. Which of the following expresses the time needed for three pools (all of the same size) to be cleaned when Joaquin and River work together?
This is a rate question, so first we should rewrite the "times" given to us as rates.
Joaquin's rate :
River's rate:
Now we add their rates together, to find the rate when they work together:
Using the equiation for distance, d = rate * time we can rearrange it to see that to find time we need to do t = distance/rate
in this case, the distance is "3 pools" and the rate is "(j+r)/jr pools per minute". So we reach our answer:
Example Question #1591 : Psat Mathematics
If Kara drives a distance of m miles every h hours, how many hours will it take her to drive a distance of d miles, in terms of m, h, and d ?
dh⁄m
d⁄hm
m⁄hd
hm⁄d
dm⁄h
dh⁄m
We need to convert d miles into hours. We do so by multiplying d miles by the conversion ratio of miles to hours given in the problem, (h hours / m miles), as follows:
d miles * (h hours / m miles) = (dh )/m hours.
From this conversion of miles into hours, we see that the number of hours it takes Kara to drive a distance of d miles is (dh )/m.
Example Question #1 : How To Find The Ratio Of A Fraction
A TV show lasts 30 minutes, what fraction of the show is left after 12 minutes have passed?
4/10
2/3
1/3
3/5
12/15
3/5
After watching 12 minutes of the show 18 remain. 18 is 60% of the total 30 minutes. As a fraction it can be expressed as 3/5.
Example Question #1 : How To Find The Ratio Of A Fraction
A bag contains red, orange, and yellow marbles only. The marbles occur in a ratio of 5 red marbles: 4 orange marbles: 1 yellow marble. If one-third of the red marbles, one-half of the orange marbles, and one-fourth of the yellow marbles are removed, then what fraction of the remaining marbles in the bag is red?
40/43
39/73
43/75
40/73
37/77
40/73
Example Question #2 : How To Find The Ratio Of A Fraction
Marty drove 40 mi/hr for 3 hours, then 60 mi/hr for 1 hour, and finally 70 mi/hr for the last 2 hours. What was Marty's average speed?
53 mi/hr
58 mi/hr
60 mi/hr
47 mi/hr
63 mi/hr
53 mi/hr
Marty's total driving time was 3 + 1 + 2 = 6 hours. He drove 40 mi/hr for 3 hours, or 3/6 = 1/2 of the time. He drove 60 mi/hr for 1 hour, or 1/6 of the drive. Lastly, he drove 70 mi/hr for 2 hours, or 2/6 = 1/3 of the drive.
To find the average speed, we need to multiply the speeds with their corresponding weights and add them up.
Average = 1/2 * 40 + 1/6 * 60 + 1/3 * 70 = 53.33... ≈ 53 mi/hr