# PSAT Math : Arithmetic

## Example Questions

### Example Question #1 : How To Find Rate

A family is on a road trip from Cleveland to Virginia Beach, totaling 600 miles. If the first half of the trip is completed in 6.5 hours and the second half of the trip is completed in 5.5 hours, what is the average speed in miles per hour of the whole trip?

Possible Answers:

45 mph

65 mph

60 mph

50 mph

55 mph

Correct answer:

50 mph

Explanation:

Take the total distance travelled (600 miles) and divide it by the total time travelled (6.5 hrs + 5.5 hrs = 12 hours) = 50 miles/hour

### Example Question #2 : How To Find Rate

Two electric cars begin moving on circular tracks at exactly 1:00pm. If the first car takes 30 minutes to complete a loop and the second car takes 40 minutes, what is the next time they will both be at the starting point?

Possible Answers:

2:40 p.m.

4:00 p.m.

3:30 p.m.

1:35 p.m.

3:00 p.m.

Correct answer:

3:00 p.m.

Explanation:

Call the cars “Car A” and “Car B”.

The least common multiple for the travel time of Car A and Car B is 120. We get the LCM by factoring. Car A’s travel time gives us 3 * 2 * 5; Car B’s time gives us 2 * 2 * 2 * 5.  The smallest number that accommodates all factors of both travel times is 2 * 2 * 2 * 3 * 5, or 120. There are 60 minutes in an hour, so 120 minutes equals two hours. Two hours after 1:00pm is 3:00pm.

### Example Question #3 : How To Find Rate

If Jon is driving his car at ten feet per second, how many feet does he travel in 30 minutes?

Possible Answers:

12,000

1800

18,000

5,800

600

Correct answer:

18,000

Explanation:

If Jon is driving at 10 feet per second he covers 10 * 60 feet in one minute (600 ft/min). In order to determine how far he travels in thirty minutes we must multiply 10 * 60 * 30 feet in 30 minutes.

### Example Question #4 : How To Find Rate

An arrow is launched at 10 meters per second. If the arrow flies at a constant velocity for an hour, how far has the arrow gone?

Possible Answers:

100 meters

36,000 meters

3600 meters

600 meters

Correct answer:

36,000 meters

Explanation:

There are 60 seconds in a minute and 60 minutes in an hour, therefore 3600 seconds in an hour. The arrow will travel 3600x10= 36,000 meters in an hour.

### Example Question #5 : How To Find Rate

If Jack ran at an average rate of 7 miles per hour for a 21 mile course, and Sam ran half as fast for the same distance, how much longer did it take for Sam to run the course than Jack?

Possible Answers:

1 hour

2.5 hours

2 hours

3 hours

4 hours

Correct answer:

3 hours

Explanation:

Using the rate formula:  Distance = Rate x Time,

Since Jack’s speed was 7 mph, Jack completed the course in 3 hours

21 = 7 x t

t = 3

Sam’s speed was half of Jack’s speed: 7/2 = 3.5

21 = 3.5 x t

t = 6

Therefore it took Sam 3 hours longer to run the course.

### Example Question #6 : How To Find Rate

If a pail collects x ounces of dripping water every 15 minutes, how many ounces will it collect in h hours?

Possible Answers:

xh

15xh

15x/h

4xh

4x/h

Correct answer:

4xh

Explanation:

Algebraic solution:  First, convert minutes to hours.

60/15 = 4, so there are 4 15-minute increments in each hour. Therefore, 4x ounces of water are collected each hour.  Multiply by h to get 4xh as the solution

Plug-in method:  Just choose numbers.

x = 2

h = 3

If 2 ounces drip in 15 minutes, how many ounces will drip in one hour?

2/15 = x/60

15x = 120

x = 8

If 8 ounces drip in one hour, how many ounces will drip in 3 hours? (remember we chose that h = 3)

3 x 8 = 24

This is the answer we are looking for.

Plug x = 2, and h = 3 into each answer choice, to determine which will work.  Remember you must plug into every answer choice in case more than one works.  In that case, choose different values for x and h, and plug into only the choices that worked the first time.

### Example Question #7 : How To Find Rate

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?

Possible Answers:

185 minutes

2.5 hours

3 hours

120 minutes

Correct answer:

3 hours

Explanation:

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 #8 : 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?

Possible Answers:

10 gallons

4 gallons

8 gallons

5 gallons

Correct answer:

5 gallons

Explanation:

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 #9 : 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?

Possible Answers:

5

10

8

None of the above

Correct answer:

8

Explanation:

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 #10 : How To Find Rate

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

Possible Answers:

6

7

6.5

8

7.5

Correct answer:

6.5

Explanation:

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