Question : A boat goes 20 km upstream and 44 km downstream in 8 hours. In 5 hours, it goes 15 km upstream and 22 km downstream. Determine the speed of the boat in still water.
Option 1: 6 km/h
Option 2: 10 km/h
Option 3: 8 km/h
Option 4: 7 km/h
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Correct Answer: 8 km/h
Solution : Let the speed of the boat in still water be $x$ km/h and The speed of stream = $y$ km/h Speed of boat at downstream = $(x+y)$ km/h Speed of boat at upstream = $(x−y)$ km/h Time taken to cover 20 km upstream = $\frac{20}{x-y}$ Time taken to cover 44 km downstream = $\frac{44}{x+y}$ According to the question, $\frac{20}{x-y}+ \frac{44}{x+y} = 8$ .......(1) Also, $\frac{15}{x-y}+ \frac{22}{x+y} = 5$ .......(2) Now let $\frac{1}{x-y} = u$ and $\frac{1}{x+y} = v$ $\therefore$ equation (1) and (2) becomes, $20u + 44v = 8$ $15u +22v = 5$ Solving these equations, we get $u = \frac{1}{5}$ $v = \frac{1}{11}$ ⇒ $x-y = 5$ and $x+y = 11$ $\therefore$ $x = 8$ and $y = 3$ The speed of the boat in still water = $x$ = 8 km/h Hence, the correct answer is 8 km/h.
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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?
Option 1: 6.5
Option 2: 7.75
Option 3: 9
Option 4: 10.5
Question : A boat moves 25 km upstream and 39 km downstream in 8 hours. It travels 35 km upstream and 52 km downstream in 11 hours. What is the speed of the stream if it travels at a uniform speed?
Option 1: 4 km/hr
Option 2: 5 km/hr
Option 3: 6 km/hr
Option 4: 3 km/hr
Question : A boat covers 35 km downstream in 2 h and covers the same distance upstream in 7 h. Find the speed (in km/h) of the boat in still water.
Option 1: 11.25
Option 2: 28.75
Option 3: 18.25
Option 4: 10.55
Question : A boat moves downstream at a rate of 8 km/hr and upstream at 4 km/hr. The speed of the boat in still water is:
Option 1: 4.5 km/hr
Option 4: 6.4 km/hr
Question : A boat can cover 120 km upstream and back in a total of 30 hours, and 25 km upstream and 40 km downstream in a total of 7 hours. How much distance will the boat cover in 16 hours in still water?
Option 1: 200 km
Option 2: 180 km
Option 3: 175 km
Option 4: 225 km
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