Question

A motorboat covers a distance of 16km upstream and 24km downstream in 6

hours. In the same time it covers a distance of 12 km upstream and 36km

downstream. Find the speed of the boat in still water and that of the​

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

... (1)

... (2)

Putting begin mathsize 12px style fraction numerator 1 over denominator straight x plus straight y end fraction equals straight u space space and space space fraction numerator begin display style 1 end style over denominator begin display style straight x minus straight y end style end fraction equals straight v end style the equations become:

24u + 16v = 6

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

36u + 12v = 6

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

Multiplying (4) by 4, we get,

24u + 8v = 4… (5)

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

12u = 1

u = begin mathsize 12px style 1 over 12 end style

Putting the value of u in (4), we get, v = begin mathsize 12px style 1 fourth end style

Thus, speed of the boat upstream = 4 km/hr

Speed of the boat downstream = 12 km/hr