Some sailors are traveling due west in a lifeboat moving 5 kilometers per hour. A rescue boat is coming due east toward them at 29 kilometers per hour. If the boats are currently 49 kilometers apart, how long will it be before they meet?

Question

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

Answer 1

To determine how long it will be before the two boats meet, we can use the concept of relative speed.

The sailors in the lifeboat are traveling at 5 kilometers per hour due west, while the rescue boat is traveling at 29 kilometers per hour due east. Since they are moving toward each other, we can add their speeds to find the relative speed.

\[ \text{Relative speed} = 5 \text{ km/h} + 29 \text{ km/h} = 34 \text{ km/h} \]

Next, we need to find out how long it will take for them to meet given that they are currently 49 kilometers apart. We can use the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the known values:

\[ \text{Time} = \frac{49 \text{ km}}{34 \text{ km/h}} \approx 1.441176 \text{ hours} \]

Now we convert the decimal time into hours and minutes. The integer part is 1 hour, and we multiply the decimal part by 60 to get the minutes:

\[ 0.441176 \text{ hours} \times 60 \text{ minutes/hour} \approx 26.47 \text{ minutes} \]

Rounding this to the nearest minute gives us approximately 26 minutes.

Thus, the time until they meet is:

\[ \text{1 hour and 26 minutes} \]

Final answer:

1 hour and 26 minutes.