A disabled sailboat is drifting on a current that is moving at $15$ kilometers per hour. Fortunately, it's drifting toward a Coast Guard station $75$ kilometers away, which picks up the distress call and sends a rescue craft directly toward the sailboat. The rescue craft can travel $53$ kilometers per hour. How long will it be before the two vessels meet? $\newline$ If necessary, round your answer to the nearest minute. $\newline$ hours and minutes

Full solution

Q. A disabled sailboat is drifting on a current that is moving at

15

kilometers per hour. Fortunately, it's drifting toward a Coast Guard station

75

kilometers away, which picks up the distress call and sends a rescue craft directly toward the sailboat. The rescue craft can travel

53

kilometers per hour. How long will it be before the two vessels meet?

\newline

If necessary, round your answer to the nearest minute.

\newline

____ hours and ____ minutes

Speed Calculation: We have: $\newline$ Speed of current (sailboat's speed): $15$ kilometers per hour $\newline$ Speed of rescue craft: $53$ kilometers per hour $\newline$ Find the combined speed of the sailboat and the rescue craft. $\newline$ Speed of sailboat + Speed of rescue craft = Combined speed $\newline$ $15 + 53 = 68$ $\newline$ Combined speed: $68$ kilometers per hour
Time Calculation: Combined speed: $68$ kilometers per hour $\newline$ Identify the time taken by the sailboat and rescue craft to cover $75$ kilometers. $\newline$ Round your answer to the nearest thousandth. $\newline$ Time $=$ Distance $/$ Combined speed $\newline$ $= 75 / 68$ $\newline$ $hickapprox 1.102941176$ hours
Conversion to Hours and Minutes: Time taken: $1.102941176$ hours $\newline$ Identify the number of hours and minutes. $\newline$ Round your answer to the nearest minute. $\newline$ In $1.102941176$ , the number of hours is $1$ . $\newline$ $(1.102941176 - 1) \times 60 = 0.102941176 \times 60 \approx 6.176$ minutes $\newline$ Rounded to the nearest minute, it is $6$ minutes. $\newline$ So, it will be $1$ hour and $6$ minutes before they meet.