Question

janine likes to draw pictures. she can draw 5 pictures of cats in 30 minutes. at what rate does janine draw cats?\
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a. \\(\frac{1\text{ picture}}{6\text{ minutes}}\\)\
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\\(\frac{6\text{ pictures}}{1\text{ minute}}\\)\
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c. 6 pictures × 1 minutes\
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d. 30 minutes × 5 pictures

Explanation:

Step1: Find time per picture

Janine draws 5 pictures in 30 minutes. To find time per picture, divide total time by number of pictures: $\frac{30\ \text{minutes}}{5\ \text{pictures}} = 6\ \text{minutes per picture}$, which is $\frac{1\ \text{picture}}{6\ \text{minutes}}$ (rate of pictures per minute? Wait, no—wait, rate here: if we want pictures per minute, it's $\frac{5}{30}=\frac{1}{6}$ pictures per minute? Wait, no, the options: A is $\frac{1\ \text{picture}}{6\ \text{minutes}}$, B is $\frac{6\ \text{pictures}}{1\ \text{minute}}$. Wait, let's recalculate.

Wait, 5 pictures in 30 minutes. So time per picture: 30 minutes / 5 pictures = 6 minutes per picture. So the rate of drawing (time per picture) is 6 minutes per 1 picture, or $\frac{1\ \text{picture}}{6\ \text{minutes}}$? Wait, no: if it's "rate" as in how many pictures per minute, it's 5/30 = 1/6 pictures per minute. But the options: A is 1 picture / 6 minutes (which is time per picture), B is 6 pictures / 1 minute (which would be 6 per minute, but 5 in 30 is 1/6 per minute). Wait, maybe the question is about time per picture. Let's check the options.

Option A: $\frac{1\ \text{picture}}{6\ \text{minutes}}$ – that means 1 picture takes 6 minutes. Let's verify: 5 pictures would take 5*6=30 minutes, which matches. So A is correct.

Step2: Eliminate other options

• Option B: $\frac{6\ \text{pictures}}{1\ \text{minute}}$ would mean 6 per minute, 5 would take 5/6 minutes, wrong.
• Option C: 6 pictures × 1 minute – doesn't make sense as a rate.
• Option D: 30 minutes × 5 pictures – multiplication, not a rate.

Answer:

A. $\frac{1\ \text{picture}}{6\ \text{minutes}}$