Daniel P. answered • 09/22/21
BS in Physics scoring in the 99th percentile on the SAT exam
Hi there Meg,
To understand this problem it is important to think about what a "rate" is. A rate generally refers to the amount of units thing 1 changes for every 1 unit of thing 2.
A common rate you are likely familiar with is miles per gallon, which can also be written as miles/gallon. This relationship means that for every gallon of gas you will travel a certain number of miles. For instance, your car might get 30 miles for every gallon of gas, which means that you could travel 30 miles for every gallon of gas that you have. If you had 2 gallons of gas, you would be able to go 60 miles since you would have twice as much gas, meaning which means you can go twice as far.
Quantities that relate to each other in this way are called proportions and are typically written as one number divided by another number, such as:
3 miles / 1 gallon
Now your question provides a rate of 2.2 feet per hour which means that for every hour that passes, the radius will grow by 2.2 feet. If we know that it will grow 2.2 feet in an hour, how much will it grow in 2 hours?
If we write it out in math form:
2.2 feet / 1 hour = rate
2 hours = duration
since we have twice as much of something we multiply by 2
(2.2 feet / 1 hour) * (2 hours / 1)
when the same unit exists above and below the divisor, they will cancel each other out leaving you left with just feet.
2.2 feet * 2
Answer = 4.4 feet
You can also intuitively think about it: 2 hours is twice as much as 1 hour, so we can multiply 2.2 feet * 2 to get 4.4 feet.
Hope that helps!
