Question

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

• A. 5
• B. 7.5
• C. 13
• D. 10

Hint:

Find downstream and upstream speeds first, then add and halve them to get the boat's own speed.

Answer 1

The Correct Option is D

Here is a second way to find the boat's speed, using the ratio of times instead of solving simultaneous equations.

The distance is the same both ways, 30 km, so speed is inversely proportional to time. Time downstream to time upstream is $2 : 6$, which simplifies to $1 : 3$. So speed downstream to speed upstream is $3 : 1$.

Let the boat speed be $x$ and the stream speed be $y$. Downstream speed is $x + y$ and upstream speed is $x - y$. From the ratio, $\frac{x+y}{x-y} = 3$, so $x + y = 3x - 3y$, which gives $4y = 2x$, or $x = 2y$.

We also know the downstream speed directly: $x + y = 30/2 = 15$. Since $x = 2y$, this becomes $2y + y = 15$, so $3y = 15$ and $y = 5$. Then $x = 2y = 10$.

Let's summarize:

• Ratio of downstream to upstream speed: 3 : 1
• Stream speed: 5 km/h
• Boat speed: $x = 10$ km/h

Both methods agree, so option D, 10 km/h, is correct.