3.00pm-10.00am=15.00-10.00=5hours
Speed of descent is 1.5 miles per hour
distance = speed x time
therefore
he has descended 1.5(5)=7.5miles
Since he has 4miles remaining
then from the start of descent, he has (7.5 + 4)miles remaining
That is at x=0, y=11.5miles
After x hours of descent, the hiker has descended 1.5x miles
So the linear equation is given by:
[tex]y(x)=11.5-1.5x[/tex]When the hiker finishes, we have distance remaining to be zero.
That is y(x)=0
[tex]\begin{gathered} \Rightarrow11.5-1.5x=0 \\ \Rightarrow-1.5x=-11.5 \\ \Rightarrow\frac{-1.5x}{-1.5}=\frac{-11.5}{-1.5} \\ \Rightarrow x=7\frac{2}{3}hours=7hours\text{ 40minutes} \end{gathered}[/tex]7hours 40minutes later from 10.00am gives 17:40, which is 5:40pm
Hence the hiker will finish at 5:40pm