#21. You work in a frame shop that specializes in handmade frames. You can make 4 large frames in 50 minutes and 6 small frames in the same amount of time. How many large frames can you make in 7 hours?

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Answer 1

To determine how many large frames can be made in 7 hours, we first need to calculate the rate of large frames made per hour.

From the information given, you can make 4 large frames in 50 minutes. To find the rate per hour, we need to convert the time from minutes to hours.

50 minutes is equivalent to \( \frac{50}{60} \) hours, which simplifies to \( \frac{5}{6} \) hours.

Now, we calculate the rate of large frames per hour:

\[ \text{Frames per hour} = \frac{\text{Number of frames}}{\text{Time in hours}} = \frac{4 \text{ frames}}{\frac{5}{6} \text{ hours}} = 4 \times \frac{6}{5} = \frac{24}{5} \text{ frames per hour} \]

Next, we want to calculate how many frames can be made in 7 hours:

\[ \text{Total large frames in 7 hours} = \text{frames per hour} \times \text{total hours} = \frac{24}{5} \times 7 \]

Calculating this gives:

\[ \text{Total large frames in 7 hours} = \frac{24 \times 7}{5} = \frac{168}{5} = 33.6 \]

Since you can't make a fraction of a frame, we round down to the nearest whole number.

Thus, the total number of large frames that can be made in 7 hours is 33 large frames.