Erick C. answered • 05/04/19
Engineer / Tutor
Lets talk about Rate. In this case, rate is the distance covered over time. This is the equation for rate:
Rate = Distance / time
In your problem the Distance is 900 feet and the time is 10 seconds. (the units are important here).
Just plug that in the equation above and you get the following:
Rate = 900ft / 10sec
Rate = 90 ft/sec
That is the value of the rate for your problem. Now lets go back to the first equation:
Rate = Distance / time
If you multiply both sides by time, you get an equation for distance:
Distance = Rate * time
Now just plug in the Rate value and we get:
Distance = 90 ft/sec * time
Distance is usually represented by x, and time is usually represented by t. Which means we can turn our equation into:
ANSWER: x = 90*t
That is your equation. However, it is very important that you ONLY use that equation when you are dealing with distance in feet and time in seconds
Additional Information:
Let's test out the equation:
If the car moves for 10 seconds, we expect it to move 900 feet. so just plug in 10 seconds in t:
x = 90 * 10
x = 900
The reason units are so important is: if you wanted to see how far the car travels in a minute. you need to convert the time to seconds:
If you put in 1 minute in the equation, it does not agree with the rate of ft/second, the units are different.
x = 90 * 1min
x = 90
that can't be right!
but if you convert the minute to seconds (1 min = 60 seconds), the answer is correct:
x = 90 * 60 sec
x = 5400
The same goes for the units of distance, the rate of 90 only works for feet. So if you're asked for a distance unit other than feet, you'll need to do a unit conversion.
quick example: you want to know how far the car moved in 1 second. but you want to know how many inches, not feet. (1 foot = 12 inches)
x = 90ft/sec * 1sec
x = 90 ft
conversion
x = 90 ft * (12 inches/ 1 ft)
x = 1080 inches
