Question

I need your help with these problems.
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Answer 1

Explanation:

(a) Hammy's rate is 36 inches in 3 sec.

(b) Hammy's unit rate is (36 inches) / (3 sec) = 12 in/sec

(c) In 5 sec Hammy can run (12 in/sec)(5 sec) = 60 in

(d) time = distance/rate, so here the time is (144 in) / (12 in/sec) = 12 sec

(6a) 4/7 divided by 3/5 is equivalent to 4/7 times 5/3, which comes out to 20/21.

(6b) Convert 2 2/5 to 12/5 and 1 7/9 to 16/9. Then invert the second improper fraction and multiply: 12/5 times 9/16 = 108/80, or 27/20.

(6c) 3.24 divided by 1.5 is equivalent to 3.24 times 2/3: 2.16, or 2 4/25

(6d) 8/9 divided by 3 1/3 is equivalent to 8/9 times 3/10, or 24/90, or 4/15.

Answer 2

I'm only doing these because it's about a pet pig named Hammy.

5.

rate = distance / time

a.

rate: 36 inches per 3 seconds

b

unit rate: 12 inches per second

c

5 seconds × 12 inches per second = 60 inches

d

144 inches / 12 inches per second = 12 seconds

6.

a.

`\frac 4 7 / \frac 3 5 = \frac 4 7 * \frac 5 3 = (20)/(21)`

b.

`2 \frac 2 5 / 1 \frac 7 9 = (12)/(5) / (16)/(9) = (12)/(5) * (9)/(16) = (27)/(20)`

c

`3.24 / 1.5 = 3.24 / \frac 3 2 = 3.24 * \frac 2 3 = 6.48/3 = 2.16`

d

`\frac 8 9 / 3\frac 1 3 = \frac 8 9 * (3)/(10) = (4)/(15)`