A boat travels 33 miles downstream in 4 hours. The return trip takes the boat 7 hours. Find the speed of the boat in still water.
Accepted Solution
A:
Answer:Speed of the boat in still water = 6.125 miles/hourStep-by-step explanation:We are given that a boat travels 33 miles downstream in 4 hours and the return trip takes the boat 7 hours.We are to find the speed of the boat in the still water.Assuming [tex]S_b[/tex] to be the speed of the boat in still water and [tex]S_w[/tex] to be the speed of the water.The speeds of the boat add up when the boat and water travel in the same direction.[tex]Speed = \frac{distance}{time}[/tex][tex]S_b+S_w=\frac{d}{t_1}=\frac{33 miles}{4 hours} [/tex]And the speed of the water is subtracted from the speed of the boat when the boat is moving upstream.[tex]S_b-S_w=\frac{d}{t_2}=\frac{33 miles}{7 hours} [/tex]Adding the two equations to get: [tex]S_b+S_w=\frac{d}{t_1}[/tex]+ [tex]S_b-S_w=\frac{d}{t_2} [/tex]___________________________[tex]2S_b=\frac{d}{t_1} +\frac{d}{t_2}[/tex]Solving this equation for [tex]S_b[/tex] and substituting the given values for [tex]d,t_1, t_2[/tex]:[tex]S_b=\frac{(t_1+t_2)d}{2t_1t_2}[/tex][tex]S_b=\frac{(4 hour + 7hour)33 mi}{2(4hour)(7hour)}[/tex][tex]S_b=\frac{(11 hour)(33mi)}{56hour^2}[/tex][tex]S_b=6.125 mi/hr[/tex]Therefore, the speed of the boat in still water is 6.125 miles/hour.