A boat takes 5 hours to go 300 km downstream. It takes the same time to go 150 km upstream. Calculate, (i) The speed of the boat in still water. (ii) The speed of the stream.?

Question

Answer

Answer

Answer: speed of the boat in still water is 45km/h

Speed of the stream is 15km/h

Step-by-step explanation: Answer:

Step-by-step explanation:Let the speed is boat is x km/h

and speed of the stream is y km/h

A/c to question, a boat takes 5 hours to go 300 km downstream.

So, speed of downstream = (x + y) km/h

So, 300/(x + y) = 5

x + y = 60....(1)

Again, it takes same time to go 150 km upstream,

So, speed of upstream = (x - y) km/h

So, 150/(x - y) = 5

x - y = 30 ....(2)

Solve equations (1) and (2),

x = 45 km/h and y = 15 km/h

Hence,the speed of boat in still water is 45km/h and speed of stream is 15km/h.

Answer

Solution:

Let the speed of the boat in still water be x km/h.

Let the speed of the stream be y km/h.

Speed downstream = (x + y) km/h
Speed upstream = (x - y) km/h

Given, time taken to travel 300 km downstream = 5 hours
Therefore, 300/(x + y) = 5
=> x + y = 60 .....(1)

Given, time taken to travel 150 km upstream = 5 hours
Therefore, 150/(x - y) = 5
=> x - y = 30 .....(2)

Adding equations (1) and (2), we get
2x = 90
=> x = 45 km/h

Substituting the value of x in equation (1), we get
45 + y = 60
=> y = 15 km/h

Therefore, (i) The speed of the boat in still water is 45 km/h.
(ii) The speed of the stream is 15 km/h.

Explanation:

This question is based on the concept of the speed of boat, speed of stream, and time taken to travel a certain distance. We are given the time taken by the boat to travel downstream as well as upstream, and the distance covered in each case. Using the formula, speed = distance/time, we can form two equations for the speed of the boat downstream and upstream, in terms of the speed of the boat in still water and the speed of the stream. By solving these equations, we can find the values of x and y, which represent the speed of the boat in still water and the speed of the stream respectively.

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