Length and Time for Nursing School Entrance Exam Study Guide (page 3)
The practice quiz for this study guide can be found at:
The United States uses the English system to measure length; however, most other countries use the metric system, which is also prevalent in scientific use in the United States. The English system requires knowing many different equivalences, but you're probably used to dealing with these equivalences on a daily basis. Mathematically, however, it's simpler to work in metric units because their equivalences are all multiples of 10. The meter is the basic unit of length, with all other length units defined in terms of the meter.
Math questions on standardized tests, especially geometry word problems, may require conversions within a particular system. An easy way to convert from one unit of measurement to another is to multiply by an equivalence ratio.
Example: Convert 3 yards to feet.
Multiply 3 yards by the ratio . Notice that we chose rather than because the yards cancel during the multiplication:
Example: Convert 31 inches to feet and inches.
|1. First, multiply 31 inches by the ratio :|
|2. Then change the portion to inches:|
|3. Thus, 31 inches is equivalent to both ft. and 2 feet 7 inches.|
Addition and Subtraction with Length Units
Finding the perimeter of a figure may require adding lengths of different units.
Example: Find the perimeter of the figure at right.
To add the lengths, add each column of length units separately:
Since 27 inches is more than 1 foot, the total of 16 ft. 27 in. must be simplified:
- Convert 27 inches to feet and inches:
- Add: 16 ft.
Thus, the perimeter is 18 feet 3 inches.
Finding the length of a line segment may require subtracting lengths of different units.
Example: Find the length of line segment AB to the right.
To subtract the lengths, subtract each column of length units separately, starting with the rightmost column.
Warning: You can't subtract 8 inches from 3 inches because 8 is larger than 3! As in regular subtraction, you have to borrow 1 from the column on the left. However, borrowing 1 ft. is the same as borrowing 12 inches; adding the borrowed 12 inches to the 3 inches gives 15 inches. Thus:
- Thus, the length of is 5 feet 7 inches.
Word problems involving time typically ask you to determine how long something takes. You might have to add together the amount of time several activities take in order to determine the total amount of time the entire process takes or calculate the elapsed time from the start to the finish of a particular activity.
Adding and subtracting time units is a lot like adding and subtracting length units. You have to make sure that you are adding hours to hours, minutes to minutes, and seconds to seconds. If the given information is in different time units, then you'll have to convert to a common time unit before you can proceed. Use the following conversion ratios:
- To convert minutes to hours:
- To convert hours to minutes:
- To convert seconds to minutes:
- To convert minutes to seconds:
Example: Convert hours to seconds.
|1. Convert hours to minutes:|
|2. Convert minutes to seconds:|
The hours and minutes cancel, giving an answer in seconds.
Calculating Elapsed Time
Calculating elapsed time when you're given the starting and ending time can be a bit tricky, depending on the starting and ending time. If the starting and ending times are both a.m. or both p.m. of the same day, you can calculate the elapsed time by simply subtracting the starting time from the ending time. However, you may have to "regroup," or "borrow."
Example: Radiology Associates opens at 6:45 a.m. and closes for lunch at 11:35 a.m. How long are they open in the morning?
|1. Set up the subtraction:|
|2. You can't subtract 45 minutes from 35 minutes, so you have to "borrow" 1 hour from the 11 hours. Borrowing 1 hour from 11 hours is equivalent to borrowing 60 minutes. Thus, you're actually subtracting 45 minutes from 95 minutes (that is, 35 + 60 minutes).|
Radiology Associates is open for 4 hours 50 minutes in the morning.
If the starting time is a.m. and ending time is p.m. of the same day, you have to calculate the elapsed time in two steps and then add the results together. Calculate the elapsed morning time by subtracting the starting time from noon. The elapsed afternoon time is equivalent to the ending time. So you add the elapsed morning time and the elapsed afternoon time to get the total elapsed time.
Example: If Radiology Associates opens at 7:15 A.M. and closes at 5:30 P.M., how long are they open?
|1. Subtract the starting time from noon:|
|(You'll have to "borrow" 60 minutes from 12.)|
|Radiology Associates is open for 4 hours 45 minutes in the morning.|
|2. Radiology Associates closes at 5:30 p.m. Thus, they're open for 5 hours 30 minutes in the afternoon.|
|3. Add the results together:|
|4. The sum of 9 hours 75 minutes needs to be adjusted because 75 minutes is more than an hour. There's a "carry" of 1 hour: the 75 minutes is equivalent to 1 hour 15 minutes. Thus, 9 hours 75 minutes is the same as 10 hours 15 minutes.|
You follow the same procedure when the starting time is P.M. of one day and the ending time is A.M. of the next day. Calculate the elapsed p.m. time by subtracting the starting time from midnight. Then add the elapsed A.M. time, which is equivalent to the ending time.
If the starting and ending times are on different days, you calculate the elapsed time in three steps: elapsed time on the starting day, elapsed time on the ending day, and the time of the intervening days. Then you add the results of the three steps together.
Example: Each week, employees of Radiology Associates turn their computers on at 6:45 A.M. on Monday and turn them off for the weekend at 5:30 P.M. on Friday. How long are the computers on, in hours?
|1. Starting day, Monday|
|a. For the A.M. hours, subtract the starting time from noon:|
|b. For the P.M. hours, there are 12 hours from noon until midnight.||12|
|c. Add the A.M. and P.M. hours to get the total hours on the starting day:|
|On Monday, 17 hours 15 minutes elapse.|
|2. Ending day, Friday|
|a. For the a.m. hours, there are 12 hours from midnight until noon:||12:00|
|b. For the p.m. hours, the ending time is the elapsed time:|
|c. Add the a.m. and p.m. hours to get the total hours on the ending day:||17:30|
|On Friday, 17 hours 30 minutes elapse.|
|3. The intervening days: Tuesday, Wednesday, and Thursday 3 days × 24 hours per day = 72 hours|
|4. Add the results of steps 1–3 together:|
|The total elapsed time is 106 hours 45 minutes.|
|5. Since the question asks for the amount of time the computers are on in hours, the 45 minutes portion of the answer must be converted to a fraction of an hour:|
|Thus, the computers were on for a total of 106 hours.|
The practice quiz for this study guide can be found at:
Washington Virtual Academies
Tuition-free online school for Washington students.
- Coats and Car Seats: A Lethal Combination?
- Kindergarten Sight Words List
- Child Development Theories
- Signs Your Child Might Have Asperger's Syndrome
- 10 Fun Activities for Children with Autism
- Why is Play Important? Social and Emotional Development, Physical Development, Creative Development
- Social Cognitive Theory
- GED Math Practice Test 1
- The Homework Debate
- First Grade Sight Words List