Question

A boat can travel 24 miles downstream in 2 hours and can make the return trip in 3 hours so what is the speed of the boat in still water and the speed of the current?

Answer 1

let speed of boat in still water be = x km/k

let speed of boat in stream be = y km/h

therefore,  in downstream speed = (x+y) km/h

while return boat will travel upstream so speed of boat in upstream = (x-y) km/h

         now time=distance/speed

• while traveling downstream speed of boat   =  2= 24/x+y ...............eq(1)
• while in upstream speed =  3= 24/x-y          .............     eq(2)

eq (1) = 2=24/x+y

2x+2y=24  ....................(eq  3)

x+y=12...........................(taking 2 as common)

taking eq (2)   3=24/x-y

3x-3y=24  ..................(eq 4)

x-y=8......................................(taking 3 as common)

solving equation (3) we get

x+y=12

x=12-y.......................(eq 5)

put eqation 5 in eq (4)

x-y=8

(12-y)-y=8

-2y=8-12

-2y=-4

y=2

put value of y in equation 5

x=12-y

x=12-2

x=10

so speed of boat in still water is 10 km/h

and in current is 2 km/h