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Learn how to figure out the area of a rectangular park when its length is three times its breadth, and someone cycling around it at 12 km/hr takes 8 minutes for one lap.
The ratio between the length and breadth of a rectangular park is 3 : 2 . If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park.
The area of the park is indeed 153600 square meters.
Given:
- Perimeter of the park is 1600 m (as calculated from the speed and time).
- Length of the park = 3x meters
- Breadth of the park = 2x meters
We have the equation for the perimeter:
Perimeter = 2(3x + 2x) = 1600
Solving for x:
2(5x) = 1600
10x = 1600
x = 160
Now, substituting x = 160 back into the expressions for length and breadth:
Length = 3x = 3 * 160 = 480 meters Breadth = 2x = 2 * 160 = 320 meters
The area of the park is:
Area = Length * Breadth = 480 * 320 = 153600 square meters.
Speed and Time Relationship in Mathematics
The relationship between speed, time, and distance is a fundamental concept in mathematics with numerous applications in various fields. Here’s a breakdown:
Formula:
- Speed (S) = Distance (D) / Time (T)
- Distance (D) = Speed (S) x Time (T)
- Time (T) = Distance (D) / Speed (S)
Proportions:
- Speed and distance are directly proportional. If you increase the speed while keeping the time constant, the distance covered will also increase. Conversely, if you decrease the speed, the distance covered will decrease.
- Speed and time are inversely proportional. If you increase the speed while keeping the distance constant, the time taken to cover that distance will decrease. Conversely, if you decrease the speed, the time taken will increase.
Real-life applications:
- Calculating travel time (e.g., how long it takes to drive from point A to point B)
- Setting race pace for runners or cyclists
- Understanding gear ratios in bicycles or cars
- Converting units of measurement (e.g., miles per hour to meters per second)
Units are crucial! When using the formulas, ensure all quantities are in compatible units (e.g., kilometers for distance, hours for time).This relationship applies to various contexts, including motion on land, air, or water.More complex scenarios might involve factors like acceleration, deceleration, and relative speed.
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Source: Math Hello Kitty
Categories: Math
