Question

A boat running upstream takes 8 hours 48 minutes to cover a certain distance while it takes 4 hours to cover the same distance running downstream what is the radio between the speed of the boat and the speed of the water current respectively

Answer 1

$let \: the \: rate \: upstream \: of \: the \: boat = x \: kmph \\ rate \: of \: down \: stream \: of \: the \: boat \: = y \: kmph$
distance travelled upstream in 8hr 48 min=distance travelled downstream in 4 hrs
since, distance=speed×time ,we have
$x + 8 \frac{4}{5} = y \times 4 \\ x \times \frac{44}{5} = y \times 4 \\ x \times \frac{11}{5} = y......eq \: (1)$
now consider the formula,
let the speed of downstream be a kmphr and the speed of upstream be km/hr
then,
$speed \: in \: Still\: water \: = 1 \div 2(a + b)kmph \\ rate \: of \: stream = 1 \div 2(a - b)kmph$
hence speed of the boat =y+X/2
speed of water=y-x/2
required ratio=(y+X/2):(y-x/2)
=(y+X):(y-x)
=(11x/5+X):(11x/5-x)
=(11x+5x):(11x-5x)
=16x:6x
=8:3....
$hope \: this \: helps \: you...$