Question

a Boat goes 32 km upstream and 36 km downstream in 7 hours and in 9 hours it can go 40 km upstream and 48 km downstream determine the speed of the stream and still water​

Answer 1

Let spead of the boat be X km/h&, &that of stream be Ykm/h

32/(X-Y)+36/(X+Y)=7

Or 32X+32Y+36X-36Y=7

Or 68X-4Y=7(X^2-Y^2)———-1)

Similarly

88X-8Y= 9(X^2-Y^2)————2)

Dividing & cross multiplying

9(68X-4Y)=7(88X-8Y)

612X-616X= 36Y-56Y———-3)

4X= 20Y

X=5Y

Putting values in equation 2

440Y-8Y= 9*24Y^2

432Y= 216Y^2

216Y= 432

Y= 2 km)h

X=10km/h Answer

Answer 2

Let the speed of boat in still water be ' x ' km / hr and that of stream be ' y ' km / hr

$speed \: = \frac{distance}{time} \\ \\ s \: = \frac{d}{t}$

( i ) Relative speed of the boat in downstream = ( x + y ) km / hr

distance travelled ( d1 ) = 36 km