a motor boat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in 4 hours 30 minutes. find the speed of the stream.

Category :

Mohammed

Guys, does anyone know the answer?

get a motor boat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in 4 hours 30 minutes. find the speed of the stream. from screen.

A motor boat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. Determine the speed of the stream.

Click here👆to get an answer to your question ✍️ A motor boat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. Determine the speed of the stream.

Question

A motor boat whose speed is 15 km/hr in still water goes 30km downstream and comes back in a total of 4 hours 30 minutes. Determine the speed of the stream.

Medium Open in App Solution Verified by Toppr

It is given that speed of motor boat in still water is 15 km/hr and total distance travelled is 30 km.

Let the speed of the stream be x km/hr then the speed upstream is (15−x) km/hr and speed downstream is (15+x) km/hr.

It is also given that total time taken is 4 hours 30 minutes, therefore,

Time taken to row down the stream is

15+x 30 and

Time taken to row up the stream is

15−x 30 Thus, we have 15+x 30 + 15−x 30 =4 2 1 ⇒ 15+x 30 + 15−x 30 = 2 9 ⇒ (15+x)(15−x) 30(15−x)+30(15+x) = 2 9 ⇒ (15) 2 −x 2 450−30x+450+30x = 2 9 (∵a 2 −b 2 =(a+b)(a−b)) ⇒ 225−x 2 900 = 2 9 ⇒2×900=9(225−x 2 ) ⇒1800=9(225−x 2 ) ⇒225−x 2 = 9 1800 ⇒225−x 2 =200 ⇒x 2 =225−200 ⇒x 2 =25 ⇒x=± 25 ⇒x=±5

Since the speed cannot be negative thus, x=5.

Hence, the speed of the stream is 5 km/hr.

Was this answer helpful?

316 16

स्रोत : www.toppr.com

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 minutes. The speed of the stream is

Byju's Answer Standard XII Mathematics

Conditions for a system of linear equations to have no solutions

A motorboat, ... Question

A motorboat, whose speed is

km/hr in still water goes

km downstream and comes back in a total of

4 hours 30

minutes. The speed of the stream is

A 4 km/hr B 6 km/hr C 10 km/hr D 5 km/hr Open in App Solution

The correct option is D

5 km/hr

Let the speed of the stream be

x km/hr Then, Speed in downstream = 15 + x km/hr Speed in upstream = 15 − x km/hr

and total time taken

= 4.5 hr ∴ 30 15 + x + 30 15 − x = 4.5 ⇒ 900 225 − x 2 = 9 2 ⇒ 225 − x 2 = 200 ⇒ x 2 = 25 ⇒ x = 5 , − 5 (rejected) ∴ x = 5 km/hr Suggest Corrections 44

[Solved] A motor boat, whose speed is 15 km/hr in still water goes 30

Given: Speed in still water = 15 km/hr Total distance = 30 km Total time = 4 hrs 30 mins = 412 hr = 9/2 hr. Formula used: Distance = Speed × Time&nbs

Home Quantitative Aptitude Speed Time and Distance Boat and River

Question

Download Solution PDF

A motor boat, whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hrs 30 mins. The speed of the stream (in km/hr) is:-

5 km/hr. 10 km/hr. 15 km/hr. 20 km/hr. 25 km/hr.

Answer (Detailed Solution Below)

Option 1 : 5 km/hr. Crack with

India's Super Teachers

FREE

Demo Classes Available*

Explore Supercoaching For FREE

Free Tests

View all Free tests >

FREE

Computer Knowledge Sectional Test 1

8.9 K Users

20 Questions 20 Marks 10 Mins

Start Now

Detailed Solution

Download Solution PDF

Given:

Speed in still water = 15 km/hr

Total distance = 30 km

Total time = 4 hrs 30 mins = 412 hr = 9/2 hr.

Formula used:

Distance = Speed × Time

Calculation:

Let the speed of the of the stream be X km/hr

Speed upstream = (15 – X) km/hr

Speed downstream = (15 + X) km/hr

According to question:

⇒ [30/(15 + x) + 30/(15 – X)] = 9/2

⇒ (450 – 30X + 450 + 30X) / (15 + X) × (15 – X) = 9/2

⇒ 900 = [(152 – X2) × 9/2]

⇒ (900 × 2/9) = 225 – X2

⇒ X2 = 225 – 200 ⇒ X2 = 25 ⇒ x = 5

∴ Speed of the stream is 5 km/hr.Key Points

If the speed of boat or swimmer is X km/hr and the speed of the stream is y km/hr then,

Speed of boat upstream = (X – Y) km/hr.

Speed of boat downstream = (X + Y) km/hr.

Download Solution PDF

Share on Whatsapp

Latest ECGC PO Updates

Last updated on Sep 22, 2022

The Export Credit Guarantee Corporation of India (ECGC) has released the ECGC PO Final Result on 2nd November. A total of 77 candidates are selected for ECGC PO (Probationary Officer) post against the total of 75 vacancies advertised. The result has been released in the form of a PDF File where you will find the roll number and registration number of the finally selected candidates. The exam was held on 29th May 2022. Also, note that the list released by the board is provisional.

Let's discuss the concepts related to Speed Time and Distance and Boat and River. Explore more from Quantitative Aptitude here. Learn now!

India’s #1 Learning Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Get Started for Free

Download App

Trusted by 3.8 Crore+ Students

‹‹ Previous Ques Next Ques ››

More Boat and River Questions

Q1. The total time taken by a boat to go 120 km upstream and came back to the starting point is 8 hours. If the speed of the stream is 25% of the speed of the boat in still water, then find the difference between the upstream speed and the downstream speed of the boat.Q2. A motor boat, whose speed is 9 km/h in still water goes 12 km down stream and comes back in a total time of 3 hours, then the speed of the stream isQ3. Swati rows downstream 24 km and 8 km upstream, and he took 4 hours each to cover both distances. Find the speed of the current.Q4. A lady row a distance of 15/4 km upstream in 3/2 hours and a distance of 13 km distance downstream in 2 hours. How much time will the lady take to row a distance of 90km in still water?Q5. A boat covers a certain distance downstream in 4 hours and returns upstream in 6 hours. If the speed of the boat in still water is 30 km/h, what is the speed of the current in km/h?Q6. A swimmer swims from a point P against the current for 6 min and then swims back along the current for next 6 min and reaches at a point Q. If the distance between P and Q is 120 m then the speed of the current (in km/h) is:Q7. If the speed of a boat in still water is 20 m / s, and speed of the current is 10 m / s, then what is the time taken by the boat to travel a distance of 6 km upstream ?Q8. A boat takes half time in moving a certain distance downstream than upstream. The ratio of the speed of the boat in still water and that of the current is?Q9. Dinesh can row at 18 Km/h in still water. If speed of stream is 6 Km/h, then how long will Dinesh take to row upto a distance of 6km and return to the starting point?Q10. The speed of the stream is 4 km/h. The time taken by a boat to cover a certain distance upstream is equal to 2.5 of the time taken by it to cover the same distance downstream. What is the speed (in km/h) of the boat in still water?

Navigation

Status

Categories

a motor boat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in 4 hours 30 minutes. find the speed of the stream.

Mohammed

A motor boat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. Determine the speed of the stream.

A motor boat whose speed is 15 km/hr in still water goes 30km downstream and comes back in a total of 4 hours 30 minutes. Determine the speed of the stream.

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 minutes. The speed of the stream is

[Solved] A motor boat, whose speed is 15 km/hr in still water goes 30

Question

A motor boat, whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hrs 30 mins. The speed of the stream (in km/hr) is:-

Answer (Detailed Solution Below)

Detailed Solution

More Boat and River Questions

More Speed Time and Distance Questions

Last Posts

Random Posts