Examkin

Question

Difficulty: EasyRelative Motion and Catch-Up Scenarios

Two motorboats leave a marina at the same time, traveling in opposite directions on a straight path. One boat travels at a constant speed of 1818 mph, and the other travels at a constant speed of 2222 mph. How many minutes will it take for the two boats to be exactly 120120 miles apart?

  1. A
    3
  2. 180Answer
  3. C
    360
  4. D
    1800

Answer

180
Because the boats are moving in opposite directions, their relative speed of separation is the sum of their individual speeds: 18 mph + 22 mph = 40 mph. To find how long it takes to separate by 120 miles, divide the distance by the relative rate: 120 / 40 = 3 hours. Finally, convert 3 hours into minutes by multiplying by 60, resulting in 180 minutes.

Step-by-Step Solution

1
Calculate the combined relative speed of the two boats.
18+22=4018 + 22 = 40 mph
Because the boats are traveling in opposite directions, their speeds add together to create the rate at which they are separating.
2
Calculate the time in hours it takes to reach the target distance.
120÷40=3120 \div 40 = 3 hours
Using the formula Time = Distance / Rate, dividing the total distance by the relative speed gives the time in hours.
3
Convert the time from hours to minutes.
3×60=1803 \times 60 = 180 minutes
The question explicitly asks for the final answer in minutes, not hours.

Key Concept

Relative Motion and Catch-Up Scenarios
Rate this question

Topics

Relative Motion and Catch-Up Scenarios

More questions from this topic