Speed of boat in still water is 12 km/hr and speed of current is 9 km/hr
Solution:
From given,
Downstream distance = 213 km
Time taken for downstream = 11 hours
Thus, speed is given as:
[tex]\text{Downstream speed} = \frac{\text{Downstream distance}}{\text{time taken}}[/tex]
[tex]\text{Downstream speed} = \frac{231}{11} = 21[/tex]
Thus downstream speed is 21 km/hr
Also,
Upstream distance = 213 km
Time taken for upstream = 77 hours
Thus, speed is given as:
[tex]\text{Upstream speed} = \frac{\text{Upstream distance}}{\text{time taken}}\\\\\text{Upstream speed} = \frac{231}{77} = 3[/tex]
Thus upstream speed is 3 km/hr
If the speed downstream is "a" km/hr and the speed upstream is "b" km/hr , then:
[tex]\text{Speed in still water } = \frac{1}{2}(a+b)\\\\\text{Speed of current } = \frac{1}{2}(a-b)[/tex]
Here, a = 21 and b = 3
Therefore,
[tex]\text{Speed in still water } = \frac{1}{2}(21+3) = \frac{24}{2} = 12\\\\\text{Speed of current } = \frac{1}{2}(21-3) = \frac{18}{2} = 9[/tex]
Thus speed of boat in still water is 12 km/hr and speed of current is 9 km/hr
