Speed of boat in still water = 25 km/hr
Speed upstream $=\dfrac{10}{1}$ = 10 km/hr
Speed of the stream = (25-10) = 15 km/hr
Speed downstream = (25+15) = 40 km/hr
Time taken to travel 10 km downstream $=\dfrac{10}{40}\text{ hours} = \dfrac{10 \times 60}{40}$ = 15 minutes
Speed downstream = (22 + 4) = 26 kmph
Time = 24 minutes $=\dfrac{24}{60}\text{ hour = }\dfrac{2}{5}\text{ hour}$
Distance travelled = Time × speed $=\dfrac{2}{5} \times 26$ = 10.4 km
Let speed of the boat in still water = a and speed of the stream = b
Then
a + b = 14
a - b = 8
Adding these two equations, we get 2a = 22
=> a = 11
ie,speed of boat in still water = 11 km/hr
Let the speed of the stream be $ x $ km/hr. Then,
Speed downstream = 15 + $ x $ km/hr,
Speed upstream = 15 - $ x $ km/hr.
| $\therefore \dfrac{30}{(15 + x)} $+$ \dfrac{30}{(15 - x)} $= 4$ \dfrac{1}{2} $ |
| $\Rightarrow$ $\dfrac{900}{(225 - x^2)}$ = $\dfrac{9}{2} $ |
$\Rightarrow$ 9$ x $2 = 225
$\Rightarrow x $2 = 25
$\Rightarrow x $ = 5 km/hr.
Speed downstream = (15 + 3) kmph = 18 kmph.
| Distance travelled =$ \left(18 \times\dfrac{12}{60} \right) $km = 3.6 km. |
speed of a boat in still water = 15 km/hr
Speed of the current = 3 km/hr
Speed downstream = (15+3) = 18 km/hr
Distance travelled downstream in 24 minutes $=\dfrac{24}{60} \times 18 = \dfrac{2 \times 18}{5}\text{ = 7.2 km}$
Speed upstream $=\dfrac{8}{\left(\dfrac{24}{60}\right)}$ = 20 km/hr
Speed of the stream = 4 km/hr
speed of boat in still water = (20+4) = 24 km/hr
Mans rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.
Mans rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.
Speed downstream = (14 + 1.2) = 15.2 kmph
Speed upstream = (14 - 1.2) = 12.8 kmph
Total time taken $=\dfrac{4864}{15.2} + \dfrac{4864}{12.8}$ = 320 + 380 = 700 hours
| Rate downstream =$ \left(\dfrac{1}{10} \times 60\right) $km/hr = 6 km/hr. |
Rate upstream = 2 km/hr.
| Speed in still water =$ \dfrac{1}{2} $(6 + 2) km/hr = 4 km/hr. |
| $\therefore$ Required time =$ \left(\dfrac{5}{4} \right) $hrs = 1$ \dfrac{1}{4} $hrs = 1 hr 15 min. |