Question

One tank is filling at at a rate of 3/4 gallon per 2/3 minutes. A second tank is filling at a rate of 5/8 gallon per 1/2 minutes. Which tank is filling faster?

Answer 1

3/4 times 3/2 (reciprocal of the second fraction) is 9/8 gallons per minute.
5/8 times 2/1 (reciprocal of the second fraction) is 10/8 gallons per minute

The second tank is filling faster.

Answer 2

Answer:

Step-by-step explanation:

Given

First tank is filling at a rate of $\frac{3}{4}$ gallon per $\frac{2}{3}$ minute i.e. per 40 sec

In 1 sec it fills $\frac{3}{4\times 40}=\frac{3}{160} gallon$

For second tank

Filling at a rate of $\frac{5}{8} per \frac{1}{2} minutes$

i.e. per 30 sec

in 1 sec it fills $\frac{5}{8\times 30}=\frac{5}{240}$

$\frac{5}{240}>{3}{160}$

thus second tank is filling at a faster rate.