A boat travels 30 km upstream in the same amount of time it takes to travel 60 km downstream in the same river. If the speed of the river is 4 km/h, find the speed of the boat in still water.?

Question

Answer

Problem:
A boat travels 30 km upstream in the same amount of time it takes to travel 60 km downstream in the same river. If the speed of the river is 4 km/h, find the speed of the boat in still water.

Solution:
Let the speed of the boat be 'x' km/h and the speed of the river be 'y' km/h.

Step 1: Write the formula for time taken to travel a certain distance.
Time = Distance/Speed

Step 2: Find the time taken to travel 30 km upstream.
Time taken to travel upstream = 30/(x-y)

Step 3: Find the time taken to travel 60 km downstream.
Time taken to travel downstream = 60/(x+y)

Step 4: Since both the times are equal, we can equate the two expressions.
30/(x-y) = 60/(x+y)

Step 5: Simplify the above expression to get an equation in 'x' and 'y'.
x^2 - y^2 = 45

Step 6: Substitute the value of 'y' in terms of the given speed of the river.
y = 4 km/h (Given)

Step 7: Simplify the equation to get an expression in terms of 'x'.
x^2 - 16 = 45

Step 8: Solve for 'x'.
x^2 = 61
x = √61 km/h

Step 9: Round off the answer to one decimal place.
x ≈ 7.8 km/h

Answer: The speed of the boat in still water is approximately 7.8 km/h.

Answer

Let the speed in still water is 'xkm/h'

So downstream speed =[x+4]km/h

and up stream speed =[x-4]km/h

So;downstream time taken to cover=60km/h

=distance/downstream speed =60/x+4 hours

for up stream=30/x-4 hours

time is same so

60/x+4=30/x-4

2/x+4=1/x-4

2x-8=x+4

2x-x=8+4

x=12km/h

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