A river ferry travels at a speed that is 300% greater in still water than the current’s speed. It covers 230 km downstream and 42 km upstream in a combined time of 15 hours. How long will the ferry take to travel 42 km upstream?

The correct answer is 3.5 hours.

Step-by-Step Explanation:

Step 1: Express the speeds in terms of the current's speed.
Let the speed of the current be $c$ km/h.
The ferry's speed in still water is 300% greater than the current's speed.
300% of $c$ is $3c$.
Therefore, the speed of the ferry in still water is:
$\text{Speed in still water}=c+3c=4c$ km/h.

Step 2: Determine downstream and upstream speeds.

When traveling downstream, the current adds to the speed of the ferry:
$\text{Downstream Speed}=4c+c=5c$ km/h.

When traveling upstream, the current opposes the speed of the ferry:
$\text{Upstream Speed}=4c-c=3c$ km/h.

Step 3: Formulate the total time equation.

Using the formula $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$:

Time taken to cover 230 km downstream:
$t_{\text{downstream}}=\frac{230}{5c}=\frac{46}{c}$ hours.

Time taken to cover 42 km upstream:
$t_{\text{upstream}}=\frac{42}{3c}=\frac{14}{c}$ hours.

The total combined time given is 15 hours:
$\frac{46}{c}+\frac{14}{c}=15$

Step 4: Solve for $c$.

$\frac{46+14}{c}=15$

$\frac{60}{c}=15$

$c=\frac{60}{15}=4$ km/h.

Step 5: Calculate the time taken to travel 42 km upstream.

The upstream speed of the ferry is:
$\text{Upstream Speed}=3c=3\times 4=12$ km/h.

The time required to travel 42 km upstream is:
$\text{Time}=\frac{42}{12}=3.5$ hours.

Thus, the ferry will take 3.5 hours to travel 42 km upstream.