Question

a motor boat whose speed is 18km/h in still water takes 1hour more to go 24km upstream to the same spot find the speed of stream.​

Answer 1

Answer:

Speed of stream is 6 km/h

Step-by-step explanation:

Given :- speed of motor boat is 18km/h

Boat travels 1hour more to go 24km up stream to the same spot .

We know that,

time = distance/speed

Let the speed of stream be x,

Then,

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

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

So,

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

• ∴24/18-x = 24/18+x + 1

• ⇒ 24/18-x - 24/18+x = 1

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

• ⇒ 48x / (18+x)(18-x) = 1

• ⇒ -x² - 48x + 324 = 0

• ⇒ x² + 48x - 324 = 0

• ⇒ x² - 6x + 54x - 324 = 0

• ⇒ x (x -6) + 54(x - 6) = 0

• ⇒ (x + 54)(x - 6) = 0

For the equation to be 0,

Either,

• ⇒ x + 54 = 0 (or) x - 6 = 0

• ⇒ x = -54 (or) x = 6

⇒ x = 6 (As speed can't be negative, x ≠ -54)

∴ The speed of stream is 6km/h

Answer 2

Speed of boat = 18 km/h

Let speed of the stream be =x km/h

Speed of upstream = ( 18 – x ) km/hr

Speed of downstream = ( 18 + x ) km/hr

Distance = 24 km

Time = Distance / Speed

As per question,

[24 / (18 – x)] – [24 / (18 + x)] = 1

24 { [1 / (18 – x)] – [1 / (18 + x) ] } = 1

[2x/(324 – x²)] = 1 / 24

324 – x² = 48

x² + 48x -324 = 0

[x +54] [x – 6] = 0

x = -54, x = 6

x = 6 km / hr

$\huge \bf \mathfrak \color{red}Speed \: \: of \: \: stream =6 km / hr$

hope it's helpful to you