A steamer, going downstream in a river, covers the distance between two towns in 20 hours. Coming back upstream, it covers this distance in 25 hours. The speed of water is 4km/h. Find the distance between the two towns.

Answer: We are given the speed of water (4 km/h) and the time taken by the steamer to travel downstream (20 hours) and upstream (25 hours). To find the distance between the two towns, we first assume the speed of the boat in still water to be x km/h. This makes the downstream speed (x+4) km/h and the upstream speed (x−4) km/h. Using the formula Distance = Speed × Time, we get two equations: distance = (x+4) × 20 and distance = (x−4) × 25. Since the distance is the same both ways, we equate them: (x+4) × 20 = (x−4) × 25. Solving this gives x=36 km/h. Putting this back into any equation, the distance comes out to be (36+4) × 20 = 800 km. So, the distance between the two towns is 800 km.

Complete Answer:

Source: ChatGPT

Let’s solve this step by step: 

Given:

• Time downstream = 20 hours
• Time upstream = 25 hours
• Speed of water = 4 km/h
• Let the speed of the steamer in still water = x km/h
• Let the distance between the two towns = D km

Step 1: Downstream and Upstream Speeds

• Downstream speed = x+4 km/h
• Upstream speed = x−4 km/h

Step 2: Use Distance = Speed × Time

• Distance going downstream:
  D = (x+4) × 20 → Equation (1)
• Distance going upstream:
  D = (x−4) × 25 → Equation (2)

Step 3: Set the two expressions for distance equal

• From Equation (1) and Equation (2):

(x+4) × 20 = (x−4) × 25

Step 4: Solve the Equation

20(x+4) = 25(x−4)

Expand both sides:

20x + 80 = 25x − 100

Bring like terms together:

80+100 = 25x − 20x ⇒ 180 = 5x ⇒ x=36

Step 5: Find the Distance

Now use the value of x=36x = 36x=36 km/h in any equation.
Using Equation (1):

D = (36+4) × 20 = 40×20 = 800 km

Therefore, the distance between the two towns is 800km.

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