An object travels x km in 20 minutes. Write down in its simplest form an expression in terms of x for its average speed in metres per second
rate = distance/time
= x km/20 min
= 1000x m/1200 seconds
= 5x/6 m/s
To find the average speed of an object, we need to convert the distance and time units into a uniform system.
Given that the object travels x km in 20 minutes, we can convert this to meters and seconds as follows:
1 km = 1000 meters
1 minute = 60 seconds
So, the distance covered by the object in meters is given by x km x 1000 meters/km = 1000x meters.
And the time taken by the object in seconds is 20 minutes x 60 seconds/minute = 1200 seconds.
Therefore, the expression for the average speed in meters per second is:
(1000x meters) / (1200 seconds) = 5/6 x meters per second
So, the average speed in simplest form is (5/6) x meters per second.
To find the average speed of the object in meters per second, we need to convert both the distance traveled and the time taken to the corresponding units.
Step 1: Convert kilometers to meters.
Since 1 kilometer is equal to 1000 meters, we can convert the distance traveled, x km, to meters by multiplying it by 1000.
Distance traveled = x km * 1000 = 1000x meters
Step 2: Convert minutes to seconds.
Since 1 minute is equal to 60 seconds, we can convert the time taken, 20 minutes, to seconds by multiplying it by 60.
Time taken = 20 minutes * 60 = 1200 seconds
Step 3: Calculate the average speed.
Average speed = Distance traveled / Time taken
Average speed = (1000x meters) / (1200 seconds)
Simplifying the expression:
To simplify the expression further, we can divide both the numerator and denominator by 200, which is the greatest common divisor.
Average speed = (1000x meters) / (1200 seconds)
Average speed = (1000/200) * (x meters) / (1200/200) seconds
Average speed = 5x meters / 6 seconds
Therefore, the expression for the average speed of the object in meters per second is (5x meters / 6 seconds).