# One tank is filling at a rate of 5/8 gallon per 7/10 hour. A second tank is filling at rate of 5/9 gallon per 2/3 hour. Which tank is filling faster?

##### 2 Answers

**Tank A** is filling faster.

#### Explanation:

You need to compare the rates in the same units to be able to decide which is better. Both are given as gallons in a fraction of an hour, but it would be better to find out how much each fills in ONE hour.

To get a RATE in 'Gallons per Hour',:

**TANK A****TANK B**

=

These are the two rates given in Gallons per Hour

A common denominator will be awkward to work with, but it is easy to make the numerators the same, and then compare.

Note that

Remember that. the bigger the denominator, the smaller the portion.

**Tank A** is filling faster.

[Decimals would have given the answer immediately, but they are not as much fun!]

Tank 1 at

#### Explanation:

The most straightforward way is to standardise the time and then just compare the rate of filling.

I chose to standardise the time to 1 hour.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

To change

So we have

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To change

so we have

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So for 1 hour the filling ratio is tank 1 : tank 2

We need to make the denominators the same. Note that

Multiply tank 2 by 1 but in the form of

So we are comparing

So tank 1 is filling faster