Question

Trisha started swimming down the Rose Springs River 3 kilometers downstream of Pine Bend. She swam at a speed of 3 kilometers per hour. At the same time, Josie started kayaking down the river 2 kilometers downstream of Pine Bend. She traveled at a speed of 5 kilometers per hour.
How many hours did it take for Josie to catch up to Trisha?
Simplify any fractions.
hours

Answer 1

Let's denote the time it takes for Josie to catch up to Trisha as \( t \) hours.

Trisha's starting point is 3 kilometers downstream of Pine Bend, and she swims at a speed of 3 kilometers per hour. Therefore, the distance she swims in \( t \) hours is:

\[
\text{Distance}_\text{Trisha} = 3 + 3t
\]

Josie's starting point is 2 kilometers downstream of Pine Bend, and she kayaks at a speed of 5 kilometers per hour. Therefore, the distance she travels in \( t \) hours is:

\[
\text{Distance}_\text{Josie} = 2 + 5t
\]

To find out when Josie catches up to Trisha, we can set the distances equal to each other:

\[
3 + 3t = 2 + 5t
\]

Now, let's solve this equation for \( t \).

Subtract \( 3t \) from both sides:

\[
3 = 2 + 5t - 3t
\]
\[
3 = 2 + 2t
\]

Next, subtract 2 from both sides:

\[
3 - 2 = 2t
\]
\[
1 = 2t
\]

Now, divide by 2:

\[
t = \frac{1}{2}
\]

Thus, the time it takes for Josie to catch up to Trisha is:

\[
\boxed{\frac{1}{2}} \text{ hours}
\]