A boat can travel at 10 km/h in still water. If it takes 2 hours to go upstream and 1 hour to return downstream, what is the speed of the current?
Practice Questions
1 question
Q1
A boat can travel at 10 km/h in still water. If it takes 2 hours to go upstream and 1 hour to return downstream, what is the speed of the current?
2 km/h
3 km/h
4 km/h
5 km/h
Let the speed of the current be x. Upstream speed = 10 - x, Downstream speed = 10 + x. Time upstream = 2 hours, Time downstream = 1 hour. Thus, 2(10 - x) = Distance and 1(10 + x) = Distance. Equating gives x = 3 km/h.
Questions & Step-by-step Solutions
1 item
Q
Q: A boat can travel at 10 km/h in still water. If it takes 2 hours to go upstream and 1 hour to return downstream, what is the speed of the current?
Solution: Let the speed of the current be x. Upstream speed = 10 - x, Downstream speed = 10 + x. Time upstream = 2 hours, Time downstream = 1 hour. Thus, 2(10 - x) = Distance and 1(10 + x) = Distance. Equating gives x = 3 km/h.
Steps: 12
Step 1: Understand that the boat's speed in still water is 10 km/h.
Step 2: Define the speed of the current as 'x'.
Step 3: Calculate the upstream speed: Upstream speed = Boat speed - Current speed = 10 - x.
Step 4: Calculate the downstream speed: Downstream speed = Boat speed + Current speed = 10 + x.
Step 5: Note that it takes 2 hours to go upstream and 1 hour to return downstream.
Step 6: Use the formula: Distance = Speed × Time. For upstream, Distance = (10 - x) × 2.
Step 7: For downstream, Distance = (10 + x) × 1.
Step 8: Since the distance is the same for both trips, set the two distance equations equal: 2(10 - x) = 1(10 + x).
Step 9: Simplify the equation: 20 - 2x = 10 + x.
Step 10: Rearrange the equation to solve for x: 20 - 10 = 2x + x, which simplifies to 10 = 3x.
Step 11: Divide both sides by 3 to find x: x = 10 / 3, which equals approximately 3.33 km/h.
Step 12: Conclude that the speed of the current is approximately 3 km/h.
