a motorboat whose speed is 18

A motor boat 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.

Given:- speed of boat = 18 k m / h r distance = 24 k m let x be the speed of stream. let t 1 and t 2 be the time for upstream and downstream. as we know that, speed = distance time ⇒ time = distance speed for upstream, speed = ( 18 − x ) k m / h r distance = 24 k m time = t 1 therefore, t 1 = 24 18 − x for downstream, speed = ( 18 + x ) k m / h r distance = 24 k m time = t 2 therefore, t 2 = 24 18 + x now according to the question- t 1 = t 2 + 1 24 18 − x = 24 18 + x + 1 ⇒ 1 18 − x − 1 18 + x = 1 24 ⇒ ( 18 + x ) − ( 18 − x ) ( 18 − x ) ( 18 + x ) = 1 24 ⇒ 48 x = ( 18 − x ) ( 18 + x ) ⇒ 48 x = 324 + 18 x − 18 x − x 2 ⇒ x 2 + 48 x − 324 = 0 ⇒ x 2 + 54 x − 6 x − 324 = 0 ⇒ x ( x + 54 ) − 6 ( x + 54 ) = 0 ⇒ ( x + 54 ) ( x − 6 ) = 0 ⇒ x = − 54 or x = 6 since speed cannot be negative. ⇒ x ≠ − 54 ∴ x = 6 thus the speed of stream is 6 k m / h r hence the correct answer is 6 k m / h r ..

A motor boat whose speed in still water is 18 km /hr, takes 1 hour more to go 24 km upstream than to return to the same spot. Find the speed of the stream.

A motor boat whose speed is 18 k m h r 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 in km/hr.​

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Question 8 A motor boat 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. Given that speed of the boat = 18 km/ hr. Let the speed of the stream = x km / hr. Given that Time taken upstream is 1 hour more than time taken downstream Time upstream = Time 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 24((18 + 𝑥) − (18 − 𝑥))/((18 − 𝑥)(18 + 𝑥)) = 1 24(18 + 𝑥 − 18 + 𝑥)/((18 − 𝑥)(18 + 𝑥)) = 1 24(2𝑥)/((18 − 𝑥)(18 + 𝑥)) = 1 48𝑥/((18 − 𝑥)(18 + 𝑥)) = 1 48x = (18 – x) (18 + x) 48x = 182 – x2 48x = 324 – x2 x2 + 48x – 324 = 0 Comparing equation with ax2 + bx + c = 0, Here a = 1, b = 48, c = –324 We know that D = b2 – 4ac D = (48)2 – 4 × 1 × (–324) D = 2304 + 4 × 324 D = 2304 + 1296 D = 3600 So, the roots to equation are x = (−𝑏 ± √𝐷)/2𝑎 Putting values x = (−(48) ± √3600)/(2 × 1) x = (− 48 ± √(60 × 60))/(2 × 1) x = (− 48 ± 60)/2 Solving So, x = 6 & x = – 54 Since, x is the speed , so it cannot be negative So, x = 6 is the solution of the equation Therefore, speed of the stream (x) = 6 km /hr.

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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

The question is a real-life application of linear equations in two variables .

Answer: The speed of the stream is 6 km/hr.

Let's explore the water currents.

Explanation:

Let the speed of the stream be x km/hr

Given that, the speed boat in still water is 18 km/hr.

Sspeed of the boat in upstream = (18 - x) km/hr

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

It is mentioned that the boat takes 1 hour more to go 24 km upstream than to return downstream to the same spot

Therefore, One-way Distance traveled by boat (d) = 24 km 

Hence, Time in hour 

T upstream  = T downstream   + 1

[distance / upstream speed ] = [distance / downstream speed]     + 1

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

[ 24/ (18 - x) - 24/ (18 + x) ] = 1 

24 [1/ (18 - x) - 1/(18 + x) ] = 1

24 [ {18 + x - (18 - x) } / {324 - x 2 } ] = 1

24 [ {18 + x - 18 + x) } / {324 - x 2 } ] = 1

⇒ 24 [ {2}x / {324 - x 2 } ] = 1

⇒ 48x = 324 - x 2

⇒ x 2  + 48x - 324 = 0

⇒ x 2  + 54x - 6x - 324 = 0   ----------> (by splitting the middle-term)

⇒ x(x + 54) - 6(x + 54) = 0

⇒ (x + 54)(x - 6) = 0

⇒ x = -54  or 6

As speed to stream can never be negative, we consider the speed of the stream (x) as 6 km/hr.

Thus, the speed of the stream is 6 km/hr.

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

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• Solution of a Quadratic Equation by...

A motor boat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km up stream that to return down stream to the same spot. Find the speed of the stream.

Let the speed of the stream be x km/hr. speed of the boat in still water = 18 km/hr. total distance = 24 km. we know that, speed of the boat up stream = speed of the boat in still water − speed of the stream = (18 − x ) km/hr speed of the boat down stream = speed of the boat in still water + speed of the stream = (18 + x ) km/hr time of up stream journey = t 1 = 24 18 - x hr time of down stream journey = t 2 = 24 18 + x hr according to the question, t 1 − t 2 = 1 hr ⇒ 24 18 - x - 24 18 + x = 1 ⇒ 24 ( 18 + x - 18 + x ) ( 18 - x ) ( 18 + x ) = 1 ⇒ 24 ( 2 x ) ( 18 ) 2 - x 2 = 1 ⇒ 48 x = 324 - x 2 ⇒ x 2 + 48 x - 324 = 0 ⇒ x 2 + 54 x - 6 x - 324 = 0 ⇒ x ( x + 54 ) - 6 ( x + 54 ) = 0 ⇒ ( x - 6 ) ( x + 54 ) = 0 ⇒ x - 6 = 0 or x + 54 = 0 ⇒ x = 6 or x = - 54 since, speed cannot be negative. thus, speed of the stream is 6 km/hr..

A motor boat whose speed in still water is 18km/hr takes 1 hour more to g 24km up stream that to return down stream to the same spot. Find the speed of the stream.

A motor boat whose speed in still water is 18 km /hr, takes 1 hour more to go 24 km upstream than to return to the same spot. Find the speed of the stream.

A motor boat whose speed is 18 k m h r 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 in km/hr.​

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