Question : A boat covers a distance of 12 km in 1 hour upstream and in 45 minutes downstream. Find the speeds of the boat and the stream (in km/hr).
Option 1: 16 and 4
Option 2: 16 and 2
Option 3: 14 and 2
Option 4: 12 and 4
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Correct Answer: 14 and 2
Solution : Let the speed of the boat be x km/hr and the speed of the stream be y km/hr. So, downstream speed = x + y = $\frac{12×60}{45}=16$ km/hr............(1) Upstream speed= x – y = 12 km/hr...........(2) By solving the above equations, we get, $\therefore$ Speed of the boat = $\frac{16+12}{2}=14$ km/hr $\therefore$ Speed of the stream = $(16 - 14) = 2$ km/hr Hence, the correct answer is 14 and 2.
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Question : A boat covers 12 km upstream and 18 km downstream in 3 hours, while it covers 36 km upstream and 24 km downstream in $6\frac{1}{2}$ hours. What is the speed of the current?
Question : A boat goes 4 km upstream and 4 km downstream in an hour. The same boat goes 5 km downstream and 3 km upstream in 55 minutes. What is the speed (in km/hr) of the boat in still water?
Question : A boat can go 5 km upstream and $7 \frac{1}{2}$ km downstream in 45 minutes. It can also go 5 km downstream and 2.5 km upstream in 25 minutes. How much time (in minutes) will it take to go 6 km upstream?
Question : A boat moves downstream at the rate of 1 km in $7\frac{1}{2}$ minutes and upstream at the rate of 5 km an hour. What is the speed of the boat in the still water?
Question : A boat covers a distance of 80 km downstream in 8 hours, while it takes 10 hours to cover the same distance upstream. What is the speed (in km/hr) of the boat in still water?
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