1. The speed of the current is 5 km/h. A boat goes 10 km upstream and back again to the starting point in 50 min. Find the speed of the boat in still water.
Sol:
d = 10
w = 5
T = 50 min = \(\frac{5}{6}\) hour
d = \(\frac{{{B^2} – {W^2}}}{{2B}} \times T\)
10 = \(\frac{{{B^2} – 25}}{{2B}} \times \frac{5}{6}\)
B² – 24B – 25 = 0
(B – 25)(B + 1) = 0
B = 25 km/h Answer
2. In a fixed time, a boy swims \(\frac{5}{2}\) times the distance along the current that he swims that he swims against the current. If the speed of the current is 6 km/h. Find the speed of the boy in still water.
Sol:
⟹ \(\frac{{B + W}}{{B – W}} = \frac{5}{2}\)
⟹ 5B – 5W = 2B + 2W
3B = 7W
3B = 7 × 6
B = 14 km/h Answer
3. The speed of a motor boat in still water is 60 km/h. If the motor boat travels 90 km along the stream in 1h 7min 30sec, then find the time taken by it to cover the same distance against the stream.
Sol:
B = 60 km/h
\(\frac{{90}}{{B + W}}\) = 1h 7min 30 sec = \(\frac{9}{8}\)
B + W = 80
60 + W = 80
W = 20 km/h
∴ upstream rate = B – W = 60 – 20 = 40 km/u
∴ tᵤₚ = \(\frac{{90}}{{40}}\) h = 2h 15 min Answer
4. Two boats A and B start towards each other from two places, 112 km apart. Speed of the boat A and B in still water are 8 km/h & 14 km/h respectively. If A proceeds downstream & B proceeds upstream then after how much time they will meet ?
Sol:
to calculate relative speed of A with respect to B, speed of water is of no use.
∴ relative speed = A + B = 8 + 1 4 = 22 km/h
∴ they will meet after = \(\frac{{112}}{{22}}\)
= \(\frac{{56}}{{11}}\) h Answer
5. A person can row 12 km/h in still water and he finds that it takes him twice as long to row up as to row down the river. Find the speed of the stream.
Sol:
B = 12 km/h
Since distance is constant
Speed ∝ \(\frac{1}{{time}}\)
\(\frac{{B – W}}{{B + W}} = \frac{1}{2}\)
⟹ B = 3W
12 = 3W
W = 4 km/h Answer
6. A boat goes 42 km upstream in 7 hours and 40 km downstream in 5 hours. Find the speed of the boat in still water.
Sol:
(B + W) × 7 = 42
B – W = 6 …………. (i)
& (B + W) × 5 = 40
B + W = 8 …………….(ii)
∴ 2B = 14
B = 7 km/h Answer
7. A man can row at a speed of 18 km/h in still water. If he takes 2 times as long to row a distance upstream as to row the same distance downstream then find the speed of the stream.
Sol:
B = 18 km/h
\(\frac{{B – W}}{{B + W}} = \frac{1}{2}\)
⟹ B = 3W
18 = 3W
W = 6 km/h Answer
8. The speed of a motor boat to that of current of water is 30 : 7. The boat goes along the current in 4h 36 min. Find the time when it will come back ?
Sol:
\(\frac{B}{W} = \frac{{30}}{7}\) 4h 36min = \(\frac{{23}}{5}\) h
distance = (30 + 7) × \(\frac{{23}}{5}\)
∴ time for upstream = \(\frac{{37 \times \frac{{23}}{5}}}{{30 – 7}}\)
= \(\frac{{37}}{5}\) h
= 7h 24 min Answer
9. The speed of a boat in still water is 8 km/h and the speed of the stream is 3 km/h. A man rows to a place at a distance of 41.25 km and comes back to the starting point. Find the total time taken by him.
Sol:
d = \(\frac{{{B^2} – {W^2}}}{{2B}} \times T\)
41.25 = \(\frac{{8 \times 8 – 3 \times 3}}{{2 \times 8}} \times T\)
T = 12 hour Answer
10. If the speed of boat in still water is 5 km/h and upstream speed is 3 km/h. Find the speed of the current.
Sol:
B = 5 km/h
B – W = 3 km/h
5 – W = 3
W = 2 km/h Answer