# a motorboat whose speed in still water is 9 km/h, goes 15 km downstream and comes back to the same spot, in a total time of 3 hours 45 minutes. find the speed of the stream.

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## A motorboat whose speed is 9 km/hr in still water, goes 15 km downstream and comes back in a total time of 3 hours 45 minutes. Find the speed of the stream.

Click here👆to get an answer to your question ✍️ A motorboat whose speed is 9 km/hr in still water, goes 15 km downstream and comes back in a total time of 3 hours 45 minutes. Find the speed of the stream.

Question

## A motorboat whose speed is 9km/hr in still water, goes 15 km downstream and comes back in a total time of 3 hours 45 minutes. Find the speed of the stream.

**A**

## 3km/hr

**B**

## 9km/hr

**C**

## 6km/hr

**D**

## 2km/hr

Medium Open in App Solution Verified by Toppr

Correct option is A)

Letspeedofstream=xkm/hr

then( 9+x 15 )+( 9−x 15 )=3+( 4 3 )hour 15( 81−x 2 9−x+9+x )=( 4 15 ) 72=81−x 2 ∴x 2 =81−72 ∴x=3km/hr

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## A motor boat whose speed in still water is 9 km / hr, goes 15 km downstream and comes back to the same spot, in a total time of 3 hours 45 minutes. Find the speed of the stream.

A motor boat whose speed in still water is 9 km / hr, goes 15 km downstream and comes back to the same spot, in a total time of 3 hours 45 minutes. Find the speed of the stream.

Byju's Answer Standard VIII Mathematics

Applications (Word Problem)

A motor boat ... Question

A motor boat whose speed in still water is 9 km/hr, goes 15 km downstream and comes back to the same spot, in a total time of 3 hours 45 minutes. Find the speed of the stream.

Open in App Solution

Let speed of stream be x km/h.

Given:

Speed of boat = 9 km/h

Distance covered upstream = 15 km

Distance covered downstream = 15 km

Total time taken = 3 hours 45 minutes =

154hours

Now, Speed of boat upstream = 9 − x km/h

Speed of boat downstream = 9 + x km/h

DistanceSpeed=Time

According to the question,

159+x+159-x=154

⇒159-x+159+x9+x9-x=154

⇒135-15x+135+15x81-x2=154

⇒135+13581-x2=154 ⇒27081-x2=154 ⇒1881-x2=14 ⇒184=81-x2 ⇒72=81-x2 ⇒x2=9 ⇒x=±3

Butxisthespeedofstreamwhichisalwayspositive.

Thus,x=3km/h

Hence, the speed of the stream is 3 km/h.

Suggest Corrections 22

SIMILAR QUESTIONS

**Q.**A motor boat whose speed is

15 k m / h r in still water goes 30

km downstream and comes back in a total of

4 hours 30

minutes. Determine the speed of the stream.

**Q.**A motorboat that has a speed of 9 km/hr in still water, goes 15 km downstream and comes back in 3 hours 45 minutes. The speed of the stream is .

**Q.**A motorboat, whose speed is

15

km/hr in still water goes

30

km downstream and comes back in a total of

4 hours 30

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**Q.**

Q12. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is-

**Q.**A motor boat has a speed of 18

k m h r

in still water. It takes 2 hours and 45 minutes more to go 66 km upstream than to return downstream to the same spot. Find the speed of the stream in

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Applications (Word Problem)

Standard VIII Mathematics

## A motorboat whose speed is 9 km\/hr in still water, goes 15 km downstream and comes back in a total time of 3 hours 45 minutes. Find the speed of the stream.(a) 3 km\/hr(b) 9 km\/hr(c) 6 km\/hr(d) 2 km\/hr

A motorboat whose speed is 9 km\/hr in still water, goes 15 km downstream and comes back in a total time of 3 hours 45 minutes. Find the speed of the stream.(a) 3 km\/hr(b) 9 km\/hr(c) 6 km\/hr(d) 2 km\/hr. Ans: Hint: To solve this problem involving ...

A motorboat whose speed is 9 km/hr in still water, goes 15 km downstream and comes back in a total time of 3 hours 45 minutes. Find the speed of the stream.(a) 3 km/hr (b) 9 km/hr (c) 6 km/hr (d) 2 km/hr

Last updated date: 13th Mar 2023

• Total views: 294.6k • Views today: 6.74k Answer Verified 294.6k+ views 1 likes

Hint: To solve this problem involving algebraic expressions, we will let the speed of the motorboat be x and the speed of the stream be y. Now, we will use the fact that when the motorboat goes upstream, the speed of the boat is (x-y) km/hr while when the motorboat goes downstream, the speed of the boat is (x+y) km/hr. We will then add up the time of their journeys upstream and downstream and equate it to 3 hours 45 minutes, to get the speed of the stream (y).

Complete step-by-step solution -

To solve the above problem, we understand the conditions given in the above problem. The speed of a motorboat in still water is 9 km/hr (x). Let the speed of the stream be y. Now, the speed of the motorboat downstream would be x+y and the speed of the motorboat upstream would be x-y (where, x = 9). Now, we are given that the motorboat goes 15 km downstream and comes back (in upstream direction) in a total time of 3 hours 45 minutes (which is

15 4 154

hours). Thus, we use the formula

Time = Distance Speed

Time = DistanceSpeed

We have, 15 x+y + 15 x−y = 15 4 15x+y+15x−y=154 Now, x = 9, thus, 15 9+y + 15 9−y = 15 4 1 9+y + 1 9−y = 1 4 9−y+9+y (9+y)(9−y) = 1 4 18 (9+y)(9−y) = 1 4

159+y+159−y=15419+y+19−y=149−y+9+y(9+y)(9−y)=1418(9+y)(9−y)=14

(9+y) (9-y) = 72 81 - y 2 y2 = 72 y 2 y2 = 9

y = 3 (y is the speed of the stream and thus cannot have negative value)

Thus, the speed of the stream is 3 km/hr.

Hence, the correct answer is (a) 3 km/hr.

Note: In most of the algebraic problems, it is important to convert the problem in English into mathematical equations. Further, while solving the equations, it is important only to pick the useful solutions from the values of variables we get. For example, in this problem, we rejected y = -3 as the solution since the speed of the stream cannot have a negative value.

Guys, does anyone know the answer?