Question

A machine can paint `340` toy boats in `45` minutes. How many boats can it paint in one hour?

Answer 1

`(340 " boats")/(3/4 " hours")`

Explanation:

Since we are asked to find the unit rate per hour, we must convert the minutes given into hours.
`45 " minutes" * (1 " hour")/(60 " minutes") = 3/4 " hours"`
Now, we simply put the number of toy boats given in the problem over the total amount of time (in hours) required to paint them. Thus, our final answer is:

`(340 " boats")/(3/4 " hours")`

Answer 2

453

Explanation:

We know that the machine paints 340 boats in 45 mins,

Therefore, there are 340 boats per 45 mins.

`"boats":"time"=340:45min`
`=340:3/4hr`

We can write this ratio as a fraction:

`340/(3/4)`

Multiplying top and bottom by 4 we get:

`(340xx4)/(4(3/4))`

`1360/3~~453.33 " toys/hr"`

So the machine can paint 453 toys per hour.

Answer 3

`453/"Hour"` from `60/45 xx 340`

Explanation:

This is a good example of the utility of "Dimensional Analysis". It ensures that the values the math generates relate to the answer that you want. We set up an equation of terms such that the result after any combinations or cancellations is in the term(s) we want.

In this case we want the rate , `"Units"/"Hour"`, and we have units per 45 minutes. We need to convert
`"Units"/"45 min"` to `"Units"/"Hour"`

So, we need a conversion of 45 minutes to hours. We could do this either as a fractional hour or minutes per hour. The minutes per hour term will illustrate the Dimensional Analysis better.

`"Units"/(cancel"min") xx cancel"min"/"Hour" = "Units"/"Hour"`

Putting our problem values into this equation we can now be sure that the result will be consistent with the desired units.
`340/45 xx (60"min")/"Hour" = 453/"Hour"`

Answer 4

`453` boats per hour
The ratio of boats : hour would be `453 : 1`

Explanation:

We need to determine how many boats are painted per hour.

In rate questions, the units indicate which values you have to divide.

We have `340` boats in `45` minutes:
Let's work with these units to start with.

`340/45` will therefore tell us how many boats per minute

There are `60` minutes in hour, so multiply by `60`
(`60` times as many boats will be painted in an hour than in a minute.)

`340/45 xx60`

`=340/3xx4`

`= 453.33`

`453` boats per hour

As a ratio:

Boats: hour

`453 : 1`

As a side comment: a ratio is a comparison between two quantities with the same type of unit, so this is more a rate than a ratio answer.