R12 Selected Answers and SolutionsSelected Answers and Solutions
The average speed was 20.04 mph. b. Divide the
distance by the average speed to fi nd the time.
_30 miles
20.04 mph^ = 1.497 hours or 1 hr 29 min 49 s
31a. The bear’s heart beats 120 times in 2 minutes
when it is active. 31b. The bear’s heart beats
18 times in 1.5 minutes when it is hibernating.
31c. the bear’s heart rate in beats per minute
31d. active: 60 beats per minute; hibernating:
12 beats per minute 31e. when it is active; Sample
answer: The active line increases faster than the
hibernating line when read from left to right.- Sometimes; a ratio that compares two
measurements with different units is a rate, such
as _10 minutes2 miles. A ratio that compares two numbers
or two measurements with like units is not a rate,
such as
2 cups
3 cups. 37. Sample answer: The rate
55 miles per hour is a measure of the number of miles
traveled per unit hour. 39. H 41. H
Pages 273–275 Lesson 5-1C
11 Make a table and compare the values. The
ratios can be simplifi ed to 225 liters. So the rates are
proportional.; Sample answer:
Time (days) 1234
Water (L) 225 450 675 900
The time to water ratio for 1, 2, 3, and 4 days is
^1
225 ,
_^2
450 or_^1
225 ,_^3
675 or_^1
225 , and_^4
900 or_^1
225. Since
these ratios are all equal to _ 2251 , the number of days
the supply lasts is proportional to the amount of
water the elephant drinks.- no; Sample answer:
Number of Teachers 4567
Number of Students 28 56 84 112
The ratio of students to teachers for 4, 5, 6, and 7
teachers is ^284 or 7, ^565 or 11.2, ^846 or 14, and ^1127 or 16.
Since these ratios are not all equal, the number of
students at the school is not proportional to the
number of teachers. - no; Sample answer:
Rental Time (h) 1234
Cost ($) 37 62 87 112
The cost to time ratio for 1, 2, 3, and 4 hours is^37 1
or 37, ^622 or 31, ^873 or 29, and ^1124 or 28. Since these
ratios are not all equal, the cost of a rental is not
proportional to the number of hours you rent the
boat. - yes; Sample answer:
Time (days) 5 101520
Length (in.) 7.5 15 22.5 30
The length to time ratio for 5, 10, 15, and 20 days
is _7.5 5 or 1.5, _^1510 or 1.5, _22.5 15 or 1.5, and _ 2030 or 1.5.
Since these ratios are all equal to 1.5 ft per day, the
length of vine is proportional to the number of
days of growth.
9a. yes; Sample answer:
Number of Hours
Worked on Sunday^1234
Number of Coupons
Given Away on Sunday^52104156208The coupons to hours ratios for 1, 2, 3, and 4 hours
of work on Sunday are _^521 or 52, _^1042 or 52, _^1563 or 52,
and _^2084 or 52. Since these ratios are all equal to
52 coupons per hour, the number of coupons given
away is proportional to the number of hours
worked on Sunday. 9b. no; Sample answer:
Number of Hours
Worked on Sunday^1234
Total Number of Coupons
Given Away that Weekend^468520572624The coupons to hours ratios for 1, 2, 3, and 4 hours
of work on Sunday are _^4681 or 468, _^5202 or 260, _^5723
or about 190, and _^6244 or 156. Since these ratios are
not all equal, the total number of coupons given
away is not proportional to the number of hours
worked on Sunday.
1111 a. Make a table and compare the side length to
the perimeter. The measures are proportional to the
perimeter. Sample answer:
Side length (units) 1234
Perimeter (units) 4 8 12 16
The side length to perimeter ratio for side lengths of
1, 2, 3, and 4 units is _ 41 , _^28 or _^14 , _ 123 or _^14 , and 16 _^4 or _^14.
Since these ratios are all equal to _^14 , the measure of
the side length of a square is proportional to the
square’s perimeter. b. Make a table and compare
the side length to the area. The measures are not
proportional to the area. Sample answer:
Side length (units) 1234
Area (units^2 ) 14916
The side length to area ratio for side lengths of 1, 2,
3, and 4 units is _ 11 or 1, _^24 or _^12 , _^39 or _^13 , and _ 164 or _^14.
Since these ratios are not all equal, the measure of
the side length of a square is not proportional to
the square’s area.- It is not proportional because the ratio of laps : time
is not consistent; ^41 ≠ 26 ≠^83 ≠ ^104.
R01_R42_EM_SelAns_895130.indd R12 1/18/10 9:51 AM