16b. Boats and still water problems step by step solution procedure and detailed explanation for each problem.

 16b.  Boats and still water  problems step by step solution procedure and detailed explanation for each problem.

Boats (Still Water):
  • Speed = Distance / Time
  • Time = Distance / Speed
  • Distance = Speed × Time

Section 2: Boats (10 Problems, Still Water)
Boat Problem 1: Basic Time Calculation
A boat travels 60 km in 4 hours in still water. Find its speed.
Step-by-Step Solution:
  1. Identify given values:
    • Distance = 60 km
    • Time = 4 hours
  2. Calculate speed: Speed = Distance / Time = 60 / 4 = 15 km/h
  3. State result: The speed is 15 km/h.
Detailed Explanation: In still water, the boat’s speed is simply distance divided by time. This basic motion problem assumes no external factors like currents, making it a straightforward application of the speed formula.
Answer: 15 km/h
Boat Problem 2: Distance Covered
A boat travels at 20 km/h in still water for 3 hours. How far does it go?
Step-by-Step Solution:
  1. Identify given values:
    • Speed = 20 km/h
    • Time = 3 hours
  2. Calculate distance: Distance = Speed × Time = 20 × 3 = 60 km
  3. State result: The distance is 60 km.
Detailed Explanation: Distance is speed multiplied by time in still water. The calculation is direct, as there’s no current affecting the boat’s speed, giving the total distance traveled.
Answer: 60 km
Boat Problem 3: Time to Cross a Lake
A boat crosses a 24 km lake at 8 km/h. How long does it take?
Step-by-Step Solution:
  1. Identify given values:
    • Distance = 24 km
    • Speed = 8 km/h
  2. Calculate time: Time = Distance / Speed = 24 / 8 = 3 hours
  3. State result: The time is 3 hours.
Detailed Explanation: Crossing a lake in still water involves dividing the distance by the boat’s speed. The result (3 hours) is the time to cover the entire distance, assuming constant speed.
Answer: 3 hours
Boat Problem 4: Round Trip Time
A boat travels 30 km to an island and back at 15 km/h. How long does the round trip take?
Step-by-Step Solution:
  1. Identify given values:
    • One-way distance = 30 km, Total distance = 30 + 30 = 60 km
    • Speed = 15 km/h
  2. Calculate total time: Time = 60 / 15 = 4 hours
  3. State result: The round trip takes 4 hours.
Detailed Explanation: The round trip distance is doubled (60 km), and the speed is constant in still water. Dividing total distance by speed gives the time, assuming no external factors like currents.
Answer: 4 hours
Boat Problem 5: Speed with Partial Time
A boat travels 18 km in 1.5 hours in still water. Find its speed.
Step-by-Step Solution:
  1. Identify given values:
    • Distance = 18 km
    • Time = 1.5 hours
  2. Calculate speed: Speed = 18 / 1.5 = 12 km/h
  3. State result: The speed is 12 km/h.
Detailed Explanation: Fractional time (1.5 hours) is handled by direct division. The speed is the distance divided by time, a simple calculation in still water with no complications from currents.
Answer: 12 km/h
Boat Problem 6: Meeting Time
Two boats start 50 km apart on a lake, traveling toward each other at 10 km/h and 15 km/h. How long until they meet?
Step-by-Step Solution:
  1. Identify given values:
    • Distance = 50 km
    • Speed 1 = 10 km/h, Speed 2 = 15 km/h
  2. Calculate relative speed: 10 + 15 = 25 km/h
  3. Calculate time: Time = 50 / 25 = 2 hours
  4. State result: They meet in 2 hours.
Detailed Explanation: In still water, the boats’ relative speed is the sum of their speeds, as they approach each other. The time to meet is the initial distance divided by relative speed, similar to trains meeting.
Answer: 2 hours
Boat Problem 7: Time with Stop
A boat travels 40 km at 16 km/h, stops for 30 minutes, then returns at 16 km/h. Find the total time.
Step-by-Step Solution:
  1. Identify given values:
    • One-way distance = 40 km, Total distance = 80 km
    • Speed = 16 km/h
    • Stop time = 30 minutes = 0.5 hours
  2. Calculate travel time: Time = 80 / 16 = 5 hours
  3. Add stop time: Total time = 5 + 0.5 = 5.5 hours
  4. State result: The total time is 5.5 hours.
Detailed Explanation: The travel time is the total distance divided by speed, and the stop time is added to account for the pause. In still water, the speed remains constant, making the calculation straightforward.
Answer: 5.5 hours
Boat Problem 8: Speed Increase
A boat travels 60 km in 5 hours. If its speed increases by 2 km/h, how long will it take to travel 60 km?
Step-by-Step Solution:
  1. Identify given values:
    • Distance = 60 km, Time = 5 hours
  2. Calculate original speed: Speed = 60 / 5 = 12 km/h
  3. Calculate new speed: 12 + 2 = 14 km/h
  4. Calculate new time: Time = 60 / 14 ≈ 4.29 hours
  5. State result: The new time is approximately 4.29 hours.
**Detailed Explanation: The original speed is calculated, then increased by 2 km/h. The new time is the distance divided by the new speed, showing how increased speed reduces travel time in still water.
Answer: ≈ 4.29 hours
Boat Problem 9: Partial Distance
A boat travels at 10 km/h for 2 hours, then 15 km/h for 1 hour. Find the total distance.
Step-by-Step Solution:
  1. Identify given values:
    • Speed 1 = 10 km/h, Time 1 = 2 hours
    • Speed 2 = 15 km/h, Time 2 = 1 hour
  2. Calculate distances:
    • Distance 1 = 10 × 2 = 20 km
    • Distance 2 = 15 × 1 = 15 km
  3. Calculate total distance: 20 + 15 = 35 km
  4. State result: The total distance is 35 km.
Detailed Explanation: Each segment’s distance is speed times time, and the total is their sum. In still water, speeds are independent, making the calculation additive.
Answer: 35 km
Boat Problem 10: Average Speed
A boat travels 48 km in 4 hours. Find the average speed.
Step-by-Step Solution:
  1. Identify given values:
    • Distance = 48 km
    • Time = 4 hours
  2. Calculate average speed: Speed = 48 / 4 = 12 km/h
  3. State result: The average speed is 12 km/h.
Detailed Explanation: Average speed in still water is total distance divided by total time, a simple division yielding 12 km/h, assuming constant conditions.
Answer: 12 km/h


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