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

Step 1: Write the downstream and upstream speeds.
Speed = distance / time. Downstream speed \(= 30/2 = 15\) km/h. Upstream speed \(= 30/6 = 5\) km/h.

Step 2: Set up equations using boat speed and stream speed.
Let the boat's speed in still water be \(x\) km/h and the stream's speed be \(y\) km/h. Downstream, the stream helps the boat, so \(x + y = 15\). Upstream, the stream slows the boat, so \(x - y = 5\).

Step 3: Solve the two equations together.
Add the equations: \((x+y) + (x-y) = 15 + 5\), which gives \(2x = 20\), so \(x = 10\). Subtract them to get \(y\): \((x+y)-(x-y)=15-5\), so \(2y=10\) and \(y=5\), though the question only asks for the boat's own speed.

Step 4: Check the wrong options.
Option A, 5, is actually the stream's speed, not the boat's. Option B, 7.5, is a rough average that ignores the correct equations. Option C, 13, does not satisfy either equation.

Final Answer:
The boat's speed in still water works out to \[ \boxed{x = 10 \text{ km/h}} \]