Question

Isabella can row a boat one mile upstream (against the current) in 22 minutes. She can row the same distance downstream in 12 minutes. Assume that both the rowing speed ans the speed of the current are constant. Determine the speed at which Isabella is rowing in still water and the speed of the current in miles per MINUTE.Isabella speed = iSpeed of current = cI know two equations 12(i+c)=1 and 22(i-c)=1Please show work.

Answer 1

Isabella speed = 0.064 mi/min

Speed of current = 0.019 mi/min

Explanation:

Let i = Isabella's speed rowing in still water

Let c = the speed of the current

i - c= her speed rowing against the current

i + c = her speed rowing with the current

We can propose the following system of equations:

`\begin{gathered} 1=(i-c)\cdot22 \\ 1=22i-22c \\ i=(1+22c)/(22)\text{ (1)} \\ 1=(i+c)\cdot12\text{ (2)} \end{gathered}`

We solve by means of the substitution method, we substitute the first equation in the second, like this:

`\begin{gathered} 1=((1+22c)/(22)+c)\cdot12 \\ 1=12\cdot((1+22c+22c)/(22)) \\ (1)/(12)\cdot22=(1+44c)/(22)\cdot22 \\ 1+44c=(22)/(12) \\ 44c=(22)/(12)-1\rightarrow44c=(22-12)/(12)\rightarrow44c=(10)/(12)\rightarrow44c=(5)/(6) \\ c=(5)/(6\cdot44) \\ c=(5)/(264)=0.019\text{ mi/min} \\ \\ \text{for i:} \\ i=(1+22\cdot0.019)/(22) \\ i=0.064\text{ mi/min} \end{gathered}`