Question

Write an equation of variation to represent the situation and solve for the missing information The time needed to travel a certain distance varies inversely with the rate of speed. If ittakes 8 hours to travel a certain distance at 36 miles per hour, how long will it take to travelthe same distance at 60 miles per hour?

Answer 1

The time needed to travel a certain distance varies inversely with the rate of speed, so:

`\begin{gathered} let\colon \\ t=\text{time} \\ v=\text{rate of speed} \\ t\propto(1)/(v) \end{gathered}`

8hours----------------------------->36mi/h

xhours----------------------------->60mi/h

`\begin{gathered} (8)/(x)=(36)/(60) \\ \text{ Since the it varies inversely:} \\ (8)/(x)=((36)/(60))^(-1) \\ (8)/(x)=(5)/(3) \\ \text{solve for x:} \\ x=(3\cdot8)/(5) \\ x=4.8h \end{gathered}`

4.8 hours or 4 hours and 48 minutes