Question

A motorboat whose speed is 18km/hr in still water
takes 1 hr more to go 24 km upstream than to
return downstream to the same spot. find the
speed of stream.​

Answer 1

let the speed of the stream be x km/h

Speed of boat upstream = speed of boat in still water -

speed of stream

= (18-x) km/h

Speed of boat downstream = speed of boat in still

water + speed of stream

= ( 18+x) km/h

$speed \: = \frac{distance}{time}$

According to the question

$\frac{24}{18 + x} + 1 = \frac{24}{18 - x } \\ \frac{24}{18 - x} - \frac{24}{18 + x} = 1 \\ \frac{24(18 + x) - 24(18 - x)}{(18 + x)(18 - x)} = 1 \\ {432 + 24x - 432 + 24x} = 324 - {x}^{2} \\ 48x = 324 - {x}^{2} \\ {x}^{2} + 48x - 324 = 0 \\ {x}^{2} + 54x - 6x - 324 = 0 \\ x(x + 54) - 6(x + 54) = 0 \\ (x + 54)(x - 6) = 0 \\ x = - 54 \: or \: 6 \\ since \: speed \: cannot \: be \: negative \\ x = 6 \\ \\ therefore \: the \: speed \: of \: the \: stream \: is \: 6km {h}^{ - 1}$

there you go :)

Answer 2

Let the speed of the stream be x km\hr.

The speed of the boat upstream = (18 - x) km/hr

The speed of the boat downstream = (18 + x) km/hr

Distance = 24 km

As given in the question,

Time for upstream = 1 + Time for downstream

24/(18 - x) = 1 + 24/(18 + x)

24/(18 - x) - 24/(18 + x) = 1

x2 + 48x - 324 = 0

(x + 54)(x - 6) = 0

x ≠ - 54 as speed cannot be negative.

x = 6

The speed of the stream = 6 km/hr