Boat and Stream LEVEL - 1
Q1–10 of 30A boat goes 8 km in one hour along the stream and 2 km in one hour against the stream. The speed in km/hr of the stream is
Downstream $= 8$ km/hr, Upstream $= 2$ km/hr
Stream speed $= \dfrac{8 - 2}{2} = 3$ km/hr
Answer: (b) 3
In one hour, a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is
Downstream $= 11$, Upstream $= 5$
Still water speed $= \dfrac{11 + 5}{2} = 8$ km/hr
Answer: (c) 8
A man rows downstream 32 km and 14 km upstream. If he takes 6 hours to cover each distance, then the velocity (in kmph) of the current is
Downstream speed $= \dfrac{32}{6} = \dfrac{16}{3}$ km/hr; Upstream speed $= \dfrac{14}{6} = \dfrac{7}{3}$ km/hr
Current $= \dfrac{\frac{16}{3} - \frac{7}{3}}{2} = \dfrac{9/3}{2} = 1.5$ km/hr
Answer: (c) $1\tfrac{1}{2}$
A boatman rows 1 km in 5 minutes, along the stream and 6 km in 1 hour against the stream. The speed of the stream is
Downstream: $1$ km in $5$ min $\Rightarrow 12$ km/hr; Upstream: $6$ km in $60$ min $= 6$ km/hr
Stream speed $= \dfrac{12 - 6}{2} = 3$ km/hr
Answer: (a) 3 kmph
A boat takes half time in moving a certain distance downstream than upstream. What is the ratio between the rate in still water and the rate of current?
Let upstream time $= 2t$, downstream time $= t \Rightarrow$ Downstream speed $= 2 \times$ Upstream speed
Take Upstream $= x$, Downstream $= 2x$
Still water $= \dfrac{2x+x}{2} = 1.5x$; Current $= \dfrac{2x-x}{2} = 0.5x$
Ratio $= 1.5x : 0.5x = 3:1$
Answer: (d)
If a man goes 18 km downstream in 4 hours and returns against the stream in 12 hours, then the speed of the stream in km/hr is
Downstream $= \dfrac{18}{4} = 4.5$ km/hr; Upstream $= \dfrac{18}{12} = 1.5$ km/hr
Stream $= \dfrac{4.5 - 1.5}{2} = 1.5$ km/hr
Answer: (b) 1.5
A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
Upstream $= 2$ km/hr; Downstream ($1$ km in $10$ min) $= 6$ km/hr
Still water $= \dfrac{6+2}{2} = 4$ km/hr
Time for $5$ km $= \dfrac{5}{4}$ hr $= 1$ hr $15$ min
Answer: (c)
A man can row $\tfrac{3}{4}$ of a km against the stream in $11\tfrac{1}{4}$ minutes and returns in $7\tfrac{1}{2}$ minutes. Find the speed of the man in still water.
Upstream $= \dfrac{3/4}{11.25/60} = 4$ km/hr; Downstream $= \dfrac{3/4}{7.5/60} = 6$ km/hr
Still water $= \dfrac{6+4}{2} = 5$ km/hr
Answer: (c) 5
A boat, while going downstream in a river covered a distance of 50 miles at an average speed of 60 miles per hour. While returning, because of the water resistance, it took 1 hour 15 minutes to cover the same distance. What was the average speed during the whole journey?
Downstream: $50$ mi at $60$ mph $\Rightarrow 50$ min. Upstream: $50$ mi in $75$ min $\Rightarrow 40$ mph
Total distance $= 100$ mi; Total time $= \dfrac{125}{60}$ hr
Average speed $= 100 \div \dfrac{125}{60} = 48$ mph
Answer: (b) 48
A man swimming in a stream which flows $1\tfrac{1}{2}$ km/hr finds that in a given time he can swim twice as far with the stream as he can against it. At what rate does he swim?
Let swim rate $= x$, current $= 1.5$
$(x+1.5) = 2(x-1.5) \Rightarrow x+1.5 = 2x-3 \Rightarrow x = 4.5$ km/hr
Answer: (a) $4\tfrac{1}{2}$