SAT Math : Arithmetic
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Example Questions
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 
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 #531 : Arithmetic
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 ?
hm⁄d
dm⁄h
m⁄hd
d⁄hm
dh⁄m
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 #43 : Fractions
A TV show lasts 30 minutes, what fraction of the show is left after 12 minutes have passed?
2/3
4/10
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 #74 : Fractions
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?
40/73
40/43
39/73
37/77
43/75
40/73
Example Question #75 : Fractions
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
47 mi/hr
63 mi/hr
60 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
Example Question #21 : Rational Numbers
A pie is made up of 
A pie is made up of 
To compute this ratio, you must first ascertain how much of the pie is jelly. This is:
Begin by using the common denominator 
So, the ratio of crust to jelly is:
This can be written as the fraction:
Example Question #52 : Fractions
In a solution, 
This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:
Remember, to divide fractions, you multiply by the reciprocal:
This is the same as saying:
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