Barbara is kayaking on a river in Clinton County, moving down the river at a speed of 8 miles per hour. Meanwhile, Levi is on a jet ski 5 miles away, moving up the river at 27 miles per hour. How long will it be before the two meet?

Question

If necessary, round your answer to the nearest minute.
hours and
minutes

Answer 1

To determine how long it will take for Barbara and Levi to meet, we need to examine their relative speeds and the distance between them.

1. Relative Speed: Since Barbara is moving downstream (with the current) at 8 miles per hour and Levi is moving upstream (against the current) at 27 miles per hour, we need to add their speeds to find their combined approach speed towards each other:

   \[ \text{Relative Speed} = \text{Speed of Levi} + \text{Speed of Barbara} = 27 \text{ mph} + 8 \text{ mph} = 35 \text{ mph} \]

2. Distance: The initial distance between them is 5 miles.

3. Time to Meet: To find the time until they meet, we can use the formula:

   \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{5 \text{ miles}}{35 \text{ mph}} \]

   \[ \text{Time} = \frac{1}{7} \text{ hours} \]

4. Converting Time into Minutes: Since we are interested in minutes, we convert \(\frac{1}{7}\) hours to minutes:

   \[ \frac{1}{7} \text{ hours} \times 60 \text{ minutes/hour} \approx 8.57 \text{ minutes} \]

Rounding \(8.57\) minutes gives approximately \(9\) minutes.

Thus, the time before they meet is approximately 0 hours and 9 minutes.