Question

A boat covers a distance of 30 kms downstream in 2 hours while it takes 6 hours to cover the same distance upstream. What is the speed of the boat in kms per hour?

• A. 5
• B. 7.5
• C. 13
• D. 10

Answer 1

The Correct Option is D

A boat covers a distance of 30 kms downstream in 2 hours while it takes 6 hours to cover the same distance upstream. What is the speed of the boat in kms per hour?

To find the speed of the boat in still water, we need to determine the speeds downstream and upstream, and use these to calculate the boat's speed. 

• Speed downstream = Distance / Time = \( \frac{30\, \text{km}}{2\, \text{hours}} = 15\, \text{km/h} \)
• Speed upstream = Distance / Time = \( \frac{30\, \text{km}}{6\, \text{hours}} = 5\, \text{km/h} \)

Let \( b \) represent the speed of the boat in still water and \( c \) the speed of the current. We have:

• Speed downstream = \( b + c = 15 \, \text{km/h} \)
• Speed upstream = \( b - c = 5 \, \text{km/h} \)

By solving these two equations, we add them to eliminate \( c \):

\((b + c) + (b - c) = 15 + 5\)

Thus,

\(2b = 20\)

\(b = 10 \, \text{km/h}\)

The speed of the boat in still water is \( \boxed{10 \, \text{km/h}} \).