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A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the current
Let’s denote the speed of the boat in still water as b km/h and the speed of the current as c km/h.
When the boat is traveling downstream, the effective speed is the sum of the speed of the boat and the speed of the current. So, the speed downstream is b + c km/h.
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When the boat is traveling upstream, the effective speed is the difference between the speed of the boat and the speed of the current. So, the speed upstream is b – c km/h.
We can use the formula:
Speed = Distance / Time
To find the speed of the boat, we have:
- b + c = 15 / 3.75 (downstream)
- b – c = 5 / 2.5 (upstream)
Solving these two equations will give us the values of b and c.
From the first equation: b + c = 15 / 3.75 = 4 km/h
From the second equation: b – c = 5 / 2.5 = 2 km/h
Now, we can solve this system of equations. Adding the two equations together, we get: 2b = 6 km/h So, b = 3 km/h.
Substituting the value of b into one of the equations, we get: 3 + c = 4 ⇒ c = 4 – 3 = 1 km/h
So, the speed of the current is 1 km/h.
Speed, Distance and Time
Speed, distance, and time are fundamental concepts used to describe the motion of objects. They are interrelated through the following formula:
Speed = Distance / Time
This formula allows you to calculate any of the three quantities, given the other two. Here’s a breakdown of each term:
- Speed: This refers to how fast an object is moving and is typically expressed in units like kilometers per hour (km/h), miles per hour (mph), or meters per second (m/s).
- Distance: This refers to the total length or gap between two points and is typically expressed in units like kilometers (km), miles (mi), or meters (m).
- Time: This refers to the duration or interval between two events and is typically expressed in units like hours (h), minutes (min), or seconds (s).
Understanding the relationship:
- Direct proportion with distance: If the speed remains constant, the greater the distance traveled, the longer the time taken (and vice versa).
- Inverse proportion with time: If the distance remains constant, the faster the speed, the less time it takes to cover the distance (and vice versa).
Example:
If a car travels 120 kilometers (distance) at a speed of 60 kilometers per hour (speed), the time taken (time) can be calculated as:
Time = Distance / Speed = 120 km / 60 km/h = 2 hours
This formula is widely used in various applications, like calculating travel times, determining average speeds, and solving motion problems in physics or engineering.
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