Measurement With Unit Rates

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ISEE Lower Level: Mathematics Achievement › Measurement With Unit Rates

Questions 1 - 10
1

A car's gas tank holds 15 gallons and it can travel 450 miles on a full tank. The car currently has 4 gallons of gas. How many miles can the car travel before it runs out of gas?

150 miles

30 miles

120 miles

180 miles

Explanation

First, find the car's fuel efficiency in miles per gallon (the unit rate). Efficiency = Total miles / Total gallons = 450 miles / 15 gallons = 30 miles per gallon. Then, multiply this rate by the amount of gas currently in the tank. Distance = 30 miles/gallon × 4 gallons = 120 miles.

2

A snail moves at a rate of 2 feet per minute. There are 3 feet in a yard. How many yards will the snail travel in one hour?

60 yards

20 yards

30 yards

40 yards

Explanation

First, find the total distance the snail moves in one hour (60 minutes) in feet. Distance in feet = 2 feet/minute × 60 minutes = 120 feet. Next, convert this distance from feet to yards using the given conversion factor. Distance in yards = 120 feet / 3 feet/yard = 40 yards.

3

A leaky faucet drips 5 milliliters of water every 10 seconds. How many liters of water will it waste in one hour? (1 liter = 1,000 milliliters)

1.8 liters

3.0 liters

30 liters

18 liters

Explanation

First, find the drip rate in milliliters per second: 5 mL / 10 seconds = 0.5 mL per second. Next, find the total seconds in an hour: 60 seconds/minute × 60 minutes/hour = 3,600 seconds. Calculate the total milliliters wasted: 0.5 mL/second × 3,600 seconds = 1,800 milliliters. Finally, convert milliliters to liters: 1,800 mL / 1,000 mL/liter = 1.8 liters.

4

A juice machine makes 18 liters of fruit punch every 6 minutes. The recipe requires 2 parts cranberry juice for every 1 part orange juice. How many liters of cranberry juice does the machine use in 10 minutes?

10 liters

30 liters

20 liters

15 liters

Explanation

First, find the rate of punch production: 18 liters / 6 minutes = 3 liters per minute. In 10 minutes, the machine makes 3 L/min × 10 min = 30 liters of punch. The recipe has 2+1=3 total parts. The fraction of cranberry juice is 2/3. So, the amount of cranberry juice is (2/3) × 30 liters = 20 liters.

5

At a farmer's market, 5 pounds of apples cost $7.50. Based on this rate, what would be the cost of 8 pounds of apples?

$10.50

$12.00

$12.50

$16.00

Explanation

First, calculate the cost per pound (the unit rate). Cost per pound = Total cost / Number of pounds = $7.50 / 5 pounds = $1.50 per pound. Then, multiply this unit rate by the desired number of pounds to find the total cost. Cost for 8 pounds = $1.50/pound × 8 pounds = $12.00.

6

A seedling is 10 centimeters tall. It grows at a steady rate of 2 centimeters every 3 days. How tall will the seedling be in 15 days?

25 cm

30 cm

16 cm

20 cm

Explanation

First, calculate the total growth over 15 days. The rate is 2 cm per 3 days. The number of 3-day periods in 15 days is 15 / 3 = 5. So, the total growth is 5 × 2 cm = 10 cm. Then, add this growth to the seedling's initial height: 10 cm (initial) + 10 cm (growth) = 20 cm.

7

If a car travels at 45 miles per hour, how long will it take to travel 90 miles?

2 hours

1 hour

45 hours

4 hours

Explanation

This question tests the ability to solve measurement problems using unit rates on the ISEE Lower Level. Understanding unit rates involves calculating how one unit relates to another, such as miles per hour or cost per item. In this specific problem, students must apply the given unit rate of 45 miles per hour to determine how long it takes to travel 90 miles. The correct answer, Choice B (2 hours), is calculated by dividing the total distance (90 miles) by the speed (45 miles per hour): 90 ÷ 45 = 2 hours, which shows a correct understanding of applying unit rates. Choice C (45 hours) is incorrect because it reflects a common student error of using the speed as the answer without performing any calculation, while Choice A (1 hour) might result from incorrectly halving the distance without considering the speed. To help students, encourage them to practice identifying unit rates in various contexts and performing calculations step-by-step. Teach students to double-check units and ensure each calculation step logically follows from the last, remembering that time = distance ÷ speed.

8

A certain type of metal weighs 5 grams per cubic centimeter. A block of this metal has a volume of 40 cubic centimeters. If this metal costs $2 per gram, what is the total cost of the block?

$80

$200

$400

$800

Explanation

This is a two-step problem. First, calculate the total weight of the metal block. Weight = Density × Volume = 5 grams/cm³ × 40 cm³ = 200 grams. Second, calculate the total cost using the price per gram. Cost = Total weight × Price per gram = 200 grams × $2/gram = $400.

9

Samantha can type 200 words in 4 minutes. She needs to type an essay that is 1,500 words long. How many minutes will it take her to type the essay?

25 minutes

30 minutes

40 minutes

35 minutes

Explanation

First, find Samantha's typing speed in words per minute. Speed = 200 words / 4 minutes = 50 words per minute. Then, divide the total number of words in the essay by her speed to find the time required. Time = 1,500 words / 50 words per minute = 30 minutes.

10

A company uses 3 pounds of ink to print 600 posters. How many pounds of ink would be needed to print 1,000 posters?

6 pounds

7 pounds

4 pounds

5 pounds

Explanation

First, find the unit rate of ink used per poster. Rate = 3 pounds / 600 posters = 0.005 pounds per poster. Then, multiply this rate by the new number of posters. Ink needed = 0.005 pounds/poster × 1,000 posters = 5 pounds. Alternatively, find posters per pound: 600/3 = 200 posters per pound. For 1,000 posters, you need 1,000/200 = 5 pounds.

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