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?
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.
