Glencoe Math: Course 2, Volume 1
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3. Convert Unit Rates
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Exercise 19 Page 31

Practice makes perfect
We are asked to find the speed of a housefly in feet per second. According to the given table, the speed of a housefly is 4.4 miles per hour. This means that we need to change miles per hour into feet per second. 4.4 mi/1 h=ft/1 sec

Let's start by organizing the relationships between the units in a table.

Starting Unit Converted Unit Unit Ratio
1 mile 5280 feet 5280ft/1mi
1 hour 60minute 60min/1h
1minute 60 seconds 60sec/1min
To perform this conversion, we need to multiply the speed in miles per hour by each unit ratio or its reciprocal. Remember, we want to arrange these ratios such that each unit we do not want gets canceled out and only the units that we want will remain.
4.4mi/1h * 5280ft/1mi * 1h/60min* 1min/60sec
4.4mi * 5280ft * 1h* 1min/1h* 1mi* 60min * 60sec
4.4 mi * 5280ft * 1 h* 1 min/1 h* 1 mi* 60 min * 60sec
4.4 * 5280ft * 1* 1/1* 1* 60 * 60sec
23 232ft/3600sec
23 232/3600* ft/sec
23 232/3600/3600/3600* ft/sec
6.453333...* ft/sec
6.45 * ft/sec
6.45ft/1sec
We got that the speed of a housefly is about 6.45 feet per second.
We want to find how many times a dragonfly's wing beats per minute. According to the given table, a dragonfly's wing beats 38 times per second, so we need to change beats per second into beats per minute. 38 beats/1 sec=beats/1 minTo do so, we will use the fact that 1 minute equals 60 seconds. Let's write this relationship as a unit ratio. 60 sec/1min To perform this conversion, we need to multiply the unit rate 38beats1sec by the unit ratio or its reciprocal. Remember, we want to arrange these ratios such that the units we do not want get canceled out and only the units that we do want remain.
38beats/1sec * 60sec/1min
38beats * 60sec/1sec* 1min
38beats * 60 sec/1 sec* 1min
38beats * 60/1* 1min
2280beats/1min
We got that a dragonfly's wing beats 2280 times per minute.
We are asked to find about how many miles a bumblebee can travel in one minute. According to the given table, the speed of a bumblebee is 6.4 miles per hour. Let's change miles per hour into miles per minute. 6.4 mi/1 h=mi/1 minTo do so, we will use the fact that 1 hour equals 60 minutes. Let's write this relationship as a unit ratio. 60 min/1h To perform this conversion, we need to multiply the speed in miles per hour by the unit ratio or its reciprocal. Remember, we want to arrange these ratios so that we can cancel out the units we do not want and keep only the units that we do want.
6.4mi/1h * 1h/60min
6.4mi * 1h/1h* 60min
6.4mi * 1 h/1 h* 60min
6.4mi * 1/1* 60min
6.4mi/60min
6.4/60* mi/min
6.4/60/60/60* mi/min
0.106666.../60/60* mi/min
0.106.../1* mi/min
0.11/1* mi/min
0.11mi/1min
We got that a bumblebee can travel about 0.11 miles in one minute.
We want to find how many times a honeybee can beat its wings in one hour. According to the given table, a honeybee's wing beats 250 times per second. We need to change beats per second into beats per hour. 250 beats/1 sec=beats/1 h

Let's start by organizing the relationships between the units in a table.

Starting Unit Converted Unit Unit Ratio
60 seconds 1minute 60sec/1min
60minutes 1 hour 60min/1h
To perform this conversion, we need to multiply the unit rate 250beats1sec by each unit ratio or its reciprocal. Remember to arrange these ratios such that the units we do not want are canceled out and only the units that we do want remain.
250beats/1sec * 60sec/1min* 60min/1h
250beats * 60sec* 60min/1sec* 1min* 1h
250beats * 60 sec* 60 min/1 sec* 1 min * 1h
250beats * 60* 60/1* 1* 1h
900 000beats/1h
We got that a honeybee beats its wings 900 000 times in one hour.