Many real-world problems ask you to deal with rates. Rates involve how fast, how long, and how many of something happens. Rates are expressed as "how many per how long" as in 10 miles per hour. Per means divide, so 10 miles per hour is 10 miles/hour.
Write 10 miles so you can cancel units laterYou could also have "gallons per hour" or even "peanuts per minute". In this lesson we are going to deal with distance (how many miles, feet, inches) using the following formula where r is the rate, t is the time and d is the distance:
This means that r = d/t and t = d/r. You can memorize all three formulas, but I think it is easier to remember just one formula (r x t = d) and then use algebra if you want to solve for r or t.
|To find||Solve for||Units will be|
|How far||d||miles, feet, km, etc.|
|How fast||r||miles per hour, feet per second, etc.|
|How long||t||hours, minutes, seconds, etc.|
Start by writing the formula: r x t = d. What are we asked for? We are asked "how far." We must solve for d. So r = 30 miles/hour, t = 2 hours.
d = 30 miles x 2 hours = 60 miles hour
Notice that the "hours" with t cancel with the denominator of r so that the resulting units are just "miles".
r x t = d
r x 20 hours = 1200 miles
r = 1200 miles / 20 hours = 60 miles / hour
t x r = d
t x 3 miles = 12 miles
t = 12 miles x hours = 4 hours
We write it like this so the miles will cancel and we are left with hours for units.
3 inches x 1 foot x 60 minutes
minute 12 inches hour
Cancel the inches and minutes and you get:
3 x 60 feet = 15 feet 12 hour hour