

1. Given the speed of the boat in still water = 5 km/hr
Let the speed of the stream = x km/hr
So, the speed of the boat upstream = (5 - x)
and the speed of the boat downstream = (5 + x)
Give, the time to cover 40 km upstream = 3* time to cover 40 km downstream
=> 40/(5 - x) = (40*3)/(5 + x)
=> 40/(5 - x) = 120/(5 + x)
=> 1/(5 - x) = 3/(5 + x)
=> 3(5 - x) = 5 + x
=> 15 - 3x = 5 + x
=> 15 - 5 = 3x + x
=> 10 = 4x
=> x = 10/4
=> x = 2.5
So, the speed of stream = 2.5 km/hr
2. Let the speed of the boat in still water is x km/hr and the speed of the stream is y km/hr
So, the speed of the boat upstream = (x - y)
and the speed of the boat downstream = (x + y)
Now, according to question,
30/(x - y) + 28/(x + y) = 7 .............1
and 21/(x - y) + 21/(x + y) = 5
=> 1/(x - y) + 1/(x + y) = 5/21 ............2
=> {1/(x - y) + 1/(x + y)}*28 = (5/21)*28
=> 28/(x - y) + 28/(x + y) = 140/21
=> 28/(x - y) + 28/(x + y) = 20/3 ............3
Now, equation 3 - eqaution 1, we get
2/(x - y) = 7 - 20/3
=> 2/(x - y) = (21 - 20)/3
=> 2/(x - y) = 1/3
=> 1/(x - y) = 1/6
=> x - y = 6 ............4
From eqaution 2, we get
1/6 + 1/(x + y) = 5/21
=> 1/(x + y) = 5/21 - 1/6
=> 1/(x + y) = (5*2 - 7*1)/42
=> 1/(x + y) = (10 - 7)/42
=> 1/(x + y) = 3/42
=> 1/(x + y) = 1/14
=> x + y = 14 ........5
After solving equation 4 and 5, we get
x = 10, y = 4
So, the speed of the boat in still water is 10 km/hr and the speed of the stream is 4 km/hr
