Question

lola and better work at a facotry that makes rubber ducks. If it takes lola 8 seconds to pain a ducky's bill red and better 10 seconds to do the same, how many seconds will it take them together to paint 36 red bills?

Answer 1

To determine how long it takes Lola and Better to paint 36 rubber ducky bills together, we first need to calculate their individual painting rates.

Lola's rate is:
- 1 bill in 8 seconds, so her rate is \( \frac{1 \text{ bill}}{8 \text{ seconds}} = \frac{1}{8} \text{ bills per second} \).

Better's rate is:
- 1 bill in 10 seconds, so his rate is \( \frac{1 \text{ bill}}{10 \text{ seconds}} = \frac{1}{10} \text{ bills per second} \).

Next, we combine their rates to find the total rate of work when they work together:
\[
\text{Combined rate} = \frac{1}{8} + \frac{1}{10}
\]

To add these fractions, we need a common denominator. The least common multiple of 8 and 10 is 40:
\[
\frac{1}{8} = \frac{5}{40}, \quad \frac{1}{10} = \frac{4}{40}
\]
Thus, adding the two rates together gives us:
\[
\text{Combined rate} = \frac{5}{40} + \frac{4}{40} = \frac{9}{40} \text{ bills per second}
\]

Now, to find the time taken to paint 36 bills, we use the formula:
\[
\text{Time} = \frac{\text{Number of bills}}{\text{Combined rate}} = \frac{36 \text{ bills}}{\frac{9}{40} \text{ bills per second}}
\]

Calculating this gives:
\[
\text{Time} = 36 \times \frac{40}{9} = \frac{1440}{9} = 160 \text{ seconds}
\]

Therefore, it will take them together **160 seconds** to paint 36 red bills.