Question

A land surveyor can survey 1 3/5 miles of a land's borders in 1 1/4 hours. How long will it take him to complete a survey for 1 mile of a land's border?

Answer 1

This problem is an example of Ratio and Proportion.
We will write the problem into the form miles / hours = miles / hours

On the first survey of the surveyor, he took 1 3/5 miles for 1 1/4 hours.
Therefore, we can write this as 1 3/5 / 1 1/4 or 8/5 / 5/4

And on his second survey, it ask how long he will take for 1 mile.
So, we will let x for the number of hours he took the survey for 1 mile.
Therefore we can write this as 1 / x.

We will now equate the two surveys.
             $\frac{ \frac{8}{5} }{ \frac{5}{4} } = \frac{1}{x}$
            $\frac{8}{5}$ × $\frac{4}{5}$ = 1 / x
                                             $\frac{32}{25} = \frac{1}{x}$
we'll do cross multiplication, and it will become
                                             32x = 25
                                                 x = 25 / 32

Therefore, it will take him 25 / 32 hours to complete a survey for 1 mile.