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A Carpenter travelled a distance of 61 km in 9 hrs. He travelled partly on foot at the rate of 4 km/hr and partly on bicycle at the rate of 9 km/hr. The distance travelled on foot is
The distance traveled on foot is 16 kilometers.
Let’s denote the distance traveled on foot as x kilometers and the distance traveled on the bicycle as 61 – x kilometers.
We know that the time taken to travel each part is the same, and we can use the formula:
Time = Distance / Speed
For the part traveled on foot: Time on foot = x / 4
For the part traveled on the bicycle: Time on bicycle = (61 – x) / 9
Given that the total time taken is 9 hours, we can set up the equation:
(x / 4) + ((61 – x) / 9) = 9
Multiplying both sides by 36 to eliminate the fractions:
9x + 4(61 – x) = 9 * 36 9x + 244 – 4x = 324 5x + 244 = 324 5x = 324 – 244 5x = 80 x = 80 / 5 x = 16
So, the distance traveled on foot is 16 kilometers.
Speed, Time and Distance
Speed, time, and distance are interrelated concepts in physics and mathematics. Here’s a brief overview:
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Speed: Speed is the rate at which an object covers distance. It is often represented as distance traveled per unit time. The standard unit of speed in the International System of Units (SI) is meters per second (m/s) or kilometers per hour (km/h). Mathematically, speed is calculated as:
Speed = Distance ÷ Time
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Time: Time is a measure of the duration between two events. It is usually measured in seconds, minutes, hours, etc. Time is often denoted by the symbol ‘t’.
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Distance: Distance is the measure of how far an object has traveled. It is the length of the path traveled by the object. Distance is typically measured in meters (m), kilometers (km), miles, etc.
Relationships between Speed, Time, and Distance:
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If you know the speed of an object and the time it travels at that speed, you can find the distance traveled using the formula: Distance = Speed × Time.
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If you know the distance traveled by an object and the time it took to travel that distance, you can find the speed using the formula: Speed = Distance ÷ Time.
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If you know the distance traveled by an object and its speed, you can find the time taken to cover that distance using the formula: Time = Distance ÷ Speed.
These relationships are fundamental in solving various problems related to motion, such as calculating travel times, finding average speeds, etc. They are extensively used in physics, engineering, and everyday life situations involving motion and travel.
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Categories: Math
