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.
[tex] \frac{ \frac{8}{5} }{ \frac{5}{4} } = \frac{1}{x} [/tex]
[tex] \frac{8}{5} [/tex] × [tex] \frac{4}{5} [/tex] = 1 / x
[tex] \frac{32}{25} = \frac{1}{x} [/tex]
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.
