Question

a motorboat cover a distance of 16 km upstream and 24km downstream in 6 hours. in the same time it cover a distance of 12km upstream and 36 km downstream. find the speed of the boat in still water and that of the strream ​

Answer 1

Answer:

Let speed of the boat in still water = x km/hr,

and

Speed of the current = y km/hr

Downstream speed = (x + y) km/hr

Upstream speed = (x − y) km/hr

$\frac{24}{x + y} + \frac{6}{x - y} = 6 - - - - (1)$

$\frac{36}{x + y} + \frac{12}{x - y } = 6 - - - (2)$

$let \: \frac{1}{x + y} = u \: and \: \: \frac{1}{x - y}$

Put in the above equation we get,

24u + 16v = 6

Or, 12u + 8v = 3 ... (3)

36u + 12v = 6

Or, 6u + 2v = 1 ... (4)

Multiplying (4) by 4, we get,

24u + 8v = 4v … (5)

Subtracting (3) by (5), we get,

12u = 1

⇒ u = 112

Putting the value of u in (4), we get, v = 1/4

$= > \frac{1}{x + y} = \frac{1}{12} and \: \frac{1}{x - y} = \frac{1}{4}$

$= > x + y = 12 \: and \: x - y = 4$

Thus, speed of the boat in still water = 8 km/hr,

Speed of the current = 4 km/hr

hope it helps you