A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of stream. 

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A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of stream.

The speed of the stream is 6 km/h.

Given:

1. Define variables:

   • Let s be the speed of the stream in km/h.
   • Let b be the speed of the motorboat in still water, which is 18 km/h as given.

2. Downstream speed:

   • The downstream speed is the sum of the boat’s speed and the stream’s speed: b + s.

3. Upstream speed:

   • The upstream speed is the difference between the boat’s speed and the stream’s speed: b – s.

4. Time difference:

   • The problem states that the upstream journey takes 1 hour longer than the downstream journey. Let t_downstream be the time taken downstream and t_upstream be the time taken upstream. We can express this as: t_upstream – t_downstream = 1.

5. Distance covered:

   • Both downstream and upstream journeys cover the same distance (24 km).

6. Relate speed, time, and distance:

   • Use the formula distance = speed x time for both downstream and upstream journeys.

7. Solve the system of equations:

   • We now have a system of four equations with four unknowns. Solve for s (the speed of the stream).

Here’s how the solution looks:

• Downstream speed: 18 + s
• Upstream speed: 18 – s
• Time difference: t_upstream – t_downstream = 1
• Distance: 24 km for both journeys

Substituting these into the distance formula and combining terms, we get:

24 / (18 + s) – 24 / (18 – s) = 1

Solving for s, we get:

s = 6 km/h

Therefore, the speed of the stream is 6 km/h.

Distance and Speed

Distance and speed are fundamental concepts in physics and everyday life.

1. Distance: Distance refers to how much ground an object has covered during its motion. It is a scalar quantity, meaning it only has magnitude and no specific direction. Distance is typically measured in units such as meters (m), kilometers (km), miles (mi), etc.

2. Speed: Speed is the rate at which an object covers distance. It is a scalar quantity as well, representing how fast something is moving without regard to its direction. Speed is calculated as the distance traveled divided by the time taken to cover that distance. Speed can be measured in units like meters per second (m/s), kilometers per hour (km/h), miles per hour (mph), etc.

The relationship between distance, speed, and time can be expressed by the formula:

Speed = Distance / Time

Or rearranging the formula:

Distance = Speed × Time

This formula shows that if you know the speed at which an object is moving and the time it has been moving at that speed, you can calculate the distance it has traveled.

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Additionally, velocity is a related concept to speed, but it includes direction. Velocity is a vector quantity, meaning it has both magnitude (speed) and direction. The same formulas apply to velocity, but with the consideration of direction. For example, if an object is moving east at 50 km/h, the velocity is 50 km/h east.

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Categories: Math