A boat can go 15 km upstream and 21 km downstream in 3 hours. If the speed of th

A boat can go 15 km upstream and 21 km downstream in 3 hours. If the speed of the boat in still water is 10 km/h, what is the speed of the stream?

A boat can go 15 km upstream and 21 km downstream in 3 hours. If the speed of the boat in still water is 10 km/h, what is the speed of the stream?

Correct Answer: 3 km/h

Step 1: Understand the problem. We have a boat that can travel upstream and downstream. We need to find the speed of the stream.
Step 2: Define the variables. Let the speed of the stream be 'x' km/h.
Step 3: Determine the speed of the boat. The speed of the boat in still water is given as 10 km/h.
Step 4: Calculate the speed of the boat upstream. The speed upstream is (10 - x) km/h because the stream slows the boat down.
Step 5: Calculate the speed of the boat downstream. The speed downstream is (10 + x) km/h because the stream helps the boat go faster.
Step 6: Write the time taken to travel upstream. The time taken to go 15 km upstream is 15/(10 - x) hours.
Step 7: Write the time taken to travel downstream. The time taken to go 21 km downstream is 21/(10 + x) hours.
Step 8: Set up the equation. The total time for both trips is 3 hours, so we write the equation: (15/(10 - x)) + (21/(10 + x)) = 3.
Step 9: Solve the equation for 'x'. This involves finding a common denominator and simplifying the equation.
Step 10: After solving, we find that x = 3 km/h, which is the speed of the stream.

Relative Speed – Understanding how the speed of a boat changes when moving upstream and downstream due to the current of the stream.
Time and Distance Relationship – Applying the formula of time = distance/speed to calculate the time taken for both upstream and downstream journeys.
Algebraic Manipulation – Solving equations involving variables to find the unknown speed of the stream.