Questions: 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

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

Transcript text: 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. $\square$ hours Submit

Solution

Solution Steps

Step 1: Determine Initial Distance

The initial distance between Trisha and Josie is calculated as follows: \[ \text{initial distance} = 3 \, \text{km} - 2 \, \text{km} = 1 \, \text{km} \]

Step 2: Calculate Relative Speed

The relative speed of Josie with respect to Trisha is given by: \[ \text{relative speed} = 5 \, \text{km/h} - 3 \, \text{km/h} = 2 \, \text{km/h} \]

Step 3: Calculate Time to Catch Up

The time it takes for Josie to catch up to Trisha is calculated using the formula: \[ \text{time to catch up} = \frac{\text{initial distance}}{\text{relative speed}} = \frac{1 \, \text{km}}{2 \, \text{km/h}} = 0.5 \, \text{hours} \]