Question

In the morning, a farm worker packed 3 pints of strawberries every 7 minutes. In the afternoon, she packed 2 pints of strawberries every 5 minutes. What was the difference between her morning and afternoon packing rates?

Answer 1

Morning:
3 pints every 7 minute = 3/7 pints/minute = 0.429 pints/minute

Afternoon:
2 pints every 5 minutes = 2/5 pints/minute = 0.4 pints/minute

Difference:
3/7 - 2/5 = 15/35 - 14/35 = 1/35 pints/minute

0.429 - 0.4 = 0.029 pints/minute

Answer 2

Answer:

She packed a pint more of strawberries every 35 minutes in the morning than that in the afternoon.

Step-by-step explanation:

We know that in the morning, she packed:

$\\ \frac{3 pints}{7min}$

And, in the afternoon:

$\\ \frac{2pints}{5min}$

How can we compare these two packing rates? How can we compare these two fractions?

The answer is equivalent fractions with the same denominator.

Additionally, we know that two fractions with the same denominator, that one with the greatest numerator is the biggest.

To convert two different fractions in equivalent fractions with the same denominator, we have to find the least common multiple (or lowest common multiple). In this case, the least common multiple of the two denominators is 7 × 5 = 35.

So, how can we express each fraction so that their common denominator is 35?

In the case of fraction $\\ \frac{3}{7}$, let us divide 35 by denominator 7:

$\\ \frac{35}{7} = 5$.

Then,

$\\ \frac{3pints}{7min} * \frac{5}{5} =\frac{15pints}{35min}$

Since $\\ \frac{5}{5} = 1$, and any number multiplied by 1 is the same number. In other words, $\\ \frac{3}{7}$ is equivalent to $\\ \frac{15}{35}$.

Similarly,

$\\ \frac{35}{5} = 7$

Thus,

$\\ \frac{2pints}{5min} * \frac{7}{7} = \frac{14pints}{35min}$.

So, we have two fractions with the same denominator:

$\\ \frac{3pints}{7min}=\frac{15pints}{35min}$, in the morning.

$\\ \frac{2pints}{5min} = \frac{14pints}{35min}$, in the afternoon.

Then, we can notice that in the morning the farmworker packed more pints of strawberries than in the afternoon:

$\\ \frac{15pints}{35min}$ > $\\ \frac{14pints}{35min}$.

That is, she packed at a rate of $\\ \frac{15pints}{35min}$ in the morning, and $\\ \frac{14pints}{35min}$ in the afternoon. That is, she was more productive in the morning than in the afternoon. But, how more productive?

We can obtain the answer after subtracting the numerators since we have fractions with the same denominators:

$\\ \frac{15pints}{35min} - \frac{14pints}{35min} = \frac{1pint}{35min}$.

Therefore, the difference between her morning and afternoon packing rates is a pint more of strawberries every 35 minutes, being more productive in the morning.