Question

An empty bucket being filled with paint at a constant rate takes $6$ minutes to be filled to $\frac{7}{10}$ of its capacity. How much more time will it take to fill the bucket to full capacity?

• A. $3\frac{2}{7}$
• B. $3\frac{3}{7}$
• C. $2\frac{3}{7}$
• D. $2\frac{4}{7}$

Answer 1

Answer: (D)

The correct option is D $2\frac{4}{7}$
Use the $RT=W$ equation to solve for the rate, with $t=6$ minutes and $w=\frac{7}{10}$:
$r\left(6minutes\right)=\frac{7}{10}$
$r=\frac{7}{10}÷=\frac{7}{60}$ buckets per minute.
Next, substitute this rate into the equation again, using $\frac{3}{10}$ for $w$ (the remaining work to be done):
$\left(\frac{7}{60}\right)t=\frac{3}{10}$
$t=\frac{3}{10}\times \frac{60}{7}=\frac{18}{7}=2\frac{4}{7}$ minutes.