# 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.

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## 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 hereπto get an answer to your question βοΈ 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 (15βx) 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 β and

Time taken to row up the stream is

15βx 30 β Thus, we have 15+x 30 β + 15βx 30 β =4 2 1 β β 15+x 30 β + 15βx 30 β = 2 9 β β (15+x)(15βx) 30(15βx)+30(15+x) β = 2 9 β β (15) 2 βx 2 450β30x+450+30x β = 2 9 β (β΅a 2 βb 2 =(a+b)(aβb)) β 225βx 2 900 β = 2 9 β β2Γ900=9(225βx 2 ) β1800=9(225βx 2 ) β225βx 2 = 9 1800 β β225βx 2 =200 βx 2 =225β200 βx 2 =25 βx=Β± 25 β βx=Β±5

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

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

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## 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

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

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

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 β x km/hr

and total time taken

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

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.**The speed of a boat in still water is

15 km/hr. It goes 30

km upstream and return downstream to the original point in

4 hrs 30

minutes. Find the speed of the stream(in km/hr).

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Conditions for a system of linear equations to have no solutions

Standard XII Mathematics

## [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 Γ Time&nbs

Home Quantitative Aptitude Speed Time and Distance Boat and River

## Question

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## 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

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## 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 Γ Time

Calculation:

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

Speed upstream = (15 β X) km/hr

Speed downstream = (15 + X) km/hr

According to question:

β [30/(15 + x) + 30/(15 β X)] = 9/2

β (450 β 30X + 450 + 30X) / (15 + X) Γ (15 β X) = 9/2

β 900 = [(152 β X2) Γ 9/2]

β (900 Γ 2/9) = 225 β X2

β X2 = 225 β 200 β X2 = 25 β x = 5

**β΄ 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 β Y) km/hr.

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

Download Solution PDF

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## 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 is

**Q3.**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?

## More Speed Time and Distance 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.**Monika covers a certain distance at the speed of 48 kmph and then she travels back at a speed of 32 kmph to go to her initial position. What is the average speed of Monika for the entire journey (in kmph)?

**Q3.**Ravi and Ajay start simultaneously from the same place A and reach at place B, 60 km apart. Ravi's speed is 4 km/hr less than that of Ajay. Ajay, after reaching place B, returns and meets Ravi at a place 12 km away from B. Find the speed (in km/hr) of Ravi.

Guys, does anyone know the answer?