Question

A hiker began his descent down a rugged mountain at 10:00 a.m. He is traveling about 1.5 miles per hour. At 3:00pm, he has 4 miles remaining in his bike.Write a linear equation to represent the distance remaining (y) in terms of hours hiked (x).What time will the hiker finish his hike?

Answer 1

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:

`y(x)=11.5-1.5x`

When the hiker finishes, we have distance remaining to be zero.

That is y(x)=0

`\begin{gathered} \Rightarrow11.5-1.5x=0 \\ \Rightarrow-1.5x=-11.5 \\ \Rightarrow(-1.5x)/(-1.5)=(-11.5)/(-1.5) \\ \Rightarrow x=7(2)/(3)hours=7hours\text{ 40minutes} \end{gathered}`

7hours 40minutes later from 10.00am gives 17:40, which is 5:40pm

Hence the hiker will finish at 5:40pm