Question

Jane took 15 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 5 min. If the current inthat part of the river is 9 km per hr, what was her boat speed in still water?Her boat speed in still water was ?km per hr.

Answer 1

Let v_b be the speed of the boat in still water; on the other hand, the relation between speed, distance, and time is

`v=(d)/(t)`

Transform minutes into hours as shown below

`\begin{gathered} (15)/(60)=0.25 \\ (5)/(60)=(1)/(12) \end{gathered}`

Therefore, in our case, the two equations are

`\begin{gathered} d=0.25(v_b-9)\rightarrow\text{ upstream} \\ d=(1)/(12)(v_b+9)\rightarrow\text{ downstream} \end{gathered}`

Thus,

`\begin{gathered} d=d \\ \Rightarrow0.25(v_b-9)=(1)/(12)(v_b+9) \\ \Rightarrow0.25v_b-2.25=(v_b)/(12)+(3)/(4) \\ \Rightarrow((1)/(4)-(1)/(12))v_b=2.25+(3)/(4) \\ \Rightarrow(1)/(6)v_b=3 \\ \Rightarrow v_b=18 \end{gathered}`

Therefore, the answer is 18km/h