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Solving Rate, Time, and Distance Equations

So, car one left New York a couple hours ago, and car two left Los Angeles one hour ago, both are going pretty fast, and you need to find out who makes it to Tulsa, Oklahoma first? These are simple! You hear the a lot on Television and such for being difficult problems, but in reality, they are easy!

Here's the only thing you'll need to remember:

Rate * Time = Distance

A simple example:

Ex 1. You are travelling 65 miles per hour; how far will you have gone after 3 hours?
Well that is pretty easy, isn't it? Your rate (speed) is 65mph, and you'll be going that fast for 3 hours (time).
This makes your equation look like: 65 * 3 = Distance. (65 * 3 = 195, and that's your answer!)

How about one of those "hard ones" that you hear on television?

Ex 2. Lisa left New York at 5AM travelling towards Chicago (790 miles away), at 65 miles per hour. Bill left Los Angeles at 6AM travelling 75 miles per hour travelling to Seattle (1135 miles away.) Who will reach their destination first?

There is nothing making this more difficult than the previous problem, except that we have to solve two problems and compare the results.

Lisa: 65 (rate) * T (unknown time) = 790 (miles to destination)
Bill: 75 (rate) * T (unknown time) = 1135 (miles to destination)

We solve both of these equations to get both of their times.

65 * T = 790; T = 790/65; T = 12.15
75 * T = 1135; T = 1135/75; T = 15.13

Who will make it to their destination first? Lisa has 12.15 hours of travel time, compared to Bill's 15.13 hours. Lisa will make it first!

Here are a couple more to try:

1. On vacation, you travelled 690 miles in 12 hours. What was your average rate of speed?
Remember: Rate * Times = Distance
We are given the Distance and Time, so we plug in the values: R * 12 = 690
Next, as with any algebra equation, we isolate the unknown value by dividing both sides by 12: R = 690/12

And our final answer is: R = 57.5 (miles per hour.)


2. It took Bob seven hours to travel 450 miles. Steve took 8 hours to travel 530 miles. Who drove faster?
First, we will look at Bob:
Rate * 7hours = 450 miles
Rate = 450/7
Bob's rate was 64.29 miles per hour.

Next, we'll determine Steve's speed:
Rate * 8hours = 530 miles
Rate = 530/8
Steve's rate was 66.25 miles per hour.

Steve drove faster!

As long as you can remember that Rate * Time = Distance, you will be able to do any of these types of problems!


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