Study Guide 5A Rates No B constructed yet.
State whether each statement is expressed as a unit rate.
1. Ernie runs 100 meters in 14 seconds.
2. During a show there are 14 commercials in 1 hour.
Solve. Show your work.
3. A machine can fill 475 bottles in 25 minutes. What is the unit rate at which the machine fills bottles?
4. A developer buys 1.4 acres of land at $37,000 per acre. How much does he pay for the land?
5. A train travels 22 miles in 15 minutes. What is the train's speed in miles per hour?
6. Water flows out of a tap at a rate of 1.2 gallons per minute. At this rate how much water will flow out of the tap in 1/2 hour?
Solve. Show your work.
7. The table shows the postage charges for sending letters to a country.
First Ounce
Each Additional Ounce
59 cents
45 cents
What is the postage for a letter weighing 7 ounces?
8. Compare the prices of vegetables below.
Which vegetable costs more per pound?
9. Ray takes 10 minutes to run 5 times around a 400-meter track. Assuming he runs at a constant speed, how long does he take to run 1 kilometer?
10. William cycles at a speed of 12 miles per hour. He cycles 10 miles from home to school. If he increases his cycling speed by 3 miles per hour, how much faster will he reach his school?
11. Mrs. Peters drives 2 hours at an average speed of 36 miles per hour. Then she drives 3 hours at a speed of 45 miles per hour. What is her average speed for the whole trip?
ANSWER KEY
1. no.
2. yes.
3. 475/25 = 19 bottles/minute
4. 37,000 x 1.4 = $51,800
5. 4 x 15 = 60 minutes; 22 x 4 = 88 miles per hour.
6. 1.2gal x 30 min = 36 gal / 1/2 hour.
7.
First Ounce
Each Additional Ounce
59 cents
45 cents
1 oz x 59 cents + 6 ounces x 45 cents = 59 + 270 =$3.29
8.
Corn: 2.70/3 = .90/pound
Peas $4.00/5 = .80/pound Corn costs more per pound.
9. 400/10 = 1000/? 400 x 2.5 = 1000 so 10 x 2.5 = 25 minutes for the kilometer.
10. William cycles at a speed of 12 miles per hour. He cycles 10 miles from home to school. If he increases his cycling speed by 3 miles per hour, how much faster will he reach his school?
Original speed:
12 miles/60 minutes. = 1 mile / 5 minutes 10 miles x 5 min/ mile = 50 minutes for 10 miles.
New speed:
12 + 3 miles / 60 minutes = 15 miles / 60 minutes = 1 mile / 4 minutes so 10 miles in 40 minutes.
50 minutes - 40 minutes is a difference of 10 minutes. He will get to school 10 minutes faster.
11. Mrs. Peters drives 2 hours at an average speed of 36 miles per hour. Then she drives 3 hours at a speed of 45 miles per hour. What is her average speed for the whole trip?
36 miles x 2 = 72 miles in 2 hours.
45 miles x 3 = 135 miles in 3 hours.
135+72 = 207 miles / 5 hours = 41.4 miles per hour average over the entire trip.