A boat can travel at 15 km/h in still water. If it takes 2 hours to travel upstr
Practice Questions
Q1
A boat can travel at 15 km/h in still water. If it takes 2 hours to travel upstream and 1.5 hours to travel downstream, what is the speed of the current?
2 km/h
3 km/h
4 km/h
5 km/h
Questions & Step-by-Step Solutions
A boat can travel at 15 km/h in still water. If it takes 2 hours to travel upstream and 1.5 hours to travel downstream, what is the speed of the current?
Step 1: Understand that the boat's speed in still water is 15 km/h.
Step 2: Define the speed of the current as 'x'.
Step 3: Calculate the upstream speed of the boat, which is the speed in still water minus the current: 15 - x.
Step 4: Calculate the downstream speed of the boat, which is the speed in still water plus the current: 15 + x.
Step 5: Use the time taken to travel upstream (2 hours) and downstream (1.5 hours) to set up equations.
Step 6: Write the equation for upstream: Distance = Speed × Time, so Distance upstream = (15 - x) × 2.
Step 7: Write the equation for downstream: Distance = Speed × Time, so Distance downstream = (15 + x) × 1.5.
Step 8: Since the distance traveled upstream and downstream is the same, set the two equations equal: (15 - x) × 2 = (15 + x) × 1.5.
Step 9: Expand both sides of the equation: 30 - 2x = 22.5 + 1.5x.
Step 10: Combine like terms to solve for 'x': 30 - 22.5 = 2x + 1.5x, which simplifies to 7.5 = 3.5x.
Step 11: Divide both sides by 3.5 to find 'x': x = 7.5 / 3.5.
Step 12: Calculate the value of 'x', which gives you the speed of the current.
Relative Speed – Understanding how the speed of a boat is affected by the current when traveling upstream and downstream.
Algebraic Manipulation – Setting up and solving equations based on the relationship between time, speed, and distance.
