Question

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

Answer 1

EXPLANATION.

• GIVEN

speed of boat in still water = 18 km/hr

Let the speed of stream = x

speed of boat upstream = 18 - x

speed of boat downstream = 18 + x

Time taken for upstream = Time taken to downstream = 1 hour

24 km upstream than to return downstream to

the same spot.

Therefore,

equation will be written as,

$\bold{\frac{24}{18 - x} = \frac{24}{18 + x} + 1}$

$\bold{24(18 + x) = 24(18 - x) + (18 - x)(18 + x)}$

$\bold{{x}^{2} + 48x - 324 = 0}$

$\bold{{x}^{2} + 54x - 6x - 324 = 0}$

$\bold{x(x + 54) - 6(x + 54) = 0}$

$\bold{(x + 54)(x - 6) = 0}$

x = 6 and x = -54

negative value will not possible

Therefore,

x = 6

Thus = x = 6 km/hr

Answer 2

$\bf \huge \underline \pink{answer}$

Given:

Speed of boat in still water = 18km/hr

Let speed of the stream = s

Speed of boat upstream = Speed of boat in still water - speed of stream = 18−s

Speed of boat down stream = Speed of boat in still water + speed of stream = 18+s

Time taken for upstream = Time taken to cover downstream + 1

$\bf \green { \implies \: \frac{24}{18 - s} = \frac{24}{18 + s} + 1}$

$\bf \green { \implies \: 24(18 + s) = 24(18 - s) + (18 - s)(18 + s)}$

$\bf \green { \implies {s}^{2} + 48s - 324 = 0}$

$\bf \green { \implies {s}^{2} + 54s - 6s - 324 = 0}$

$\bf \green { \implies(s + 54)(s - 6) = 0}$

$\bf \red { \implies \: s = 6 \: and \: - 54}$

$\bf \green{s≠ - 54}$

Thus, s=6 km/he speed of stream cannot be negative...