To do this, we'll subtract from both sides. On the right side, it means subtracting from Our next step is to group like terms—remember, our eventual goal is to have t on the left side of the equals sign and a number on the right.
We'll cancel out the t on the right side by adding 30 t to both sides. On the right side, we'll add it to t. Finally, to get t on its own, we'll divide each side by its coefficient: So t is equal to 3. In other words, the time Bill traveled on the interstate is equal to 3 hours.
Remember, we're ultimately trying to find the distanc e Bill traveled on the interstate. Let's look at the interstate row of our chart again and see if we have enough information to find out. It looks like we do. Now that we're only missing one variable, we should be able to find its value pretty quickly. We now know that Bill traveled on the interstate for 3 hours at 70 mph , so we can fill in this information. Finally, we finished simplifying the right side of the equation.
We have the answer to our problem! The distance is In other words, Bill drove miles on the interstate. It might have seemed like it took a long time to solve the first problem. The more practice you get with these problems, the quicker they'll go. Let's try a similar problem. This one is called a round-trip problem because it describes a round trip—a trip that includes a return journey.
Even though the trip described in this problem is slightly different from the one in our first problem, you should be able to solve it the same way. Let's take a look:. Eva drove to work at an average speed of 36 mph.
On the way home, she hit traffic and only drove an average of 27 mph. Her total time in the car was 1 hour and 45 minutes, or 1. How far does Eva live from work? If you're having trouble understanding this problem, you might want to visualize Eva's commute like this:. As always, let's start by filling in a table with the important information. We'll make a row with information about her trip to work and from work.
Remember, the total travel time is 1. In both equations, d represents the total distance. From the diagram, you can see that these two equations are equal to each other—after all, Eva drives the same distance to and from work. Just like with the last problem we solved, we can solve this one by combining the two equations. Since the value of d is 36 t , we can replace any occurrence of d with 36 t.
Now, let's simplify the right side. Next, we'll cancel out t by adding 27 t to both sides of the equation.
Finally, we can get t on its own by dividing both sides by its coefficient: In other words, the time it took Eva to drive to work is. Now that we know the value of t , we'll be able to can find the distance to Eva's work. If you guessed that we were going to use the travel equation again, you were right. We now know the value of two out of the three variables, which means we know enough to solve our problem.
First, let's fill in the values we know. We'll work with the numbers for the trip to work. We already knew the rate : And we just learned the time :.
In other words, the distance to Eva's work is 27 miles. Our problem is solved. An intersecting distance problem is one where two things are moving toward each other.
Here's a typical problem:. Pawnee and Springfield are miles apart. A train leaves Pawnee heading to Springfield at the same time a train leaves Springfield heading to Pawnee. One train is moving at a speed of 45 mph, and the other is moving 60 mph. How long will they travel before they meet? This problem is asking you to calculate how long it will take these two trains moving toward each other to cross paths.
This might seem confusing at first. Even though it's a real-world situation, it can be difficult to imagine distance and motion abstractly. This diagram might help you get a sense of what this situation looks like:. If you're still confused, don't worry! You can solve this problem the same way you solved the two-part problems on the last page. You'll just need a chart and the travel formula. A train leaves Pawnee heading toward Springfield at the same time a train leaves Springfield heading toward Pawnee.
One train is moving at a speed of 45 mph , and the other is moving 60 mph. Let's start by filling in our chart. Here's the problem again, this time with the important information underlined. How do you find time with distance and speed? Solving for time. Rate of change in position, or speed, is equal to distance traveled divided by time. To solve for time, divide the distance traveled by the rate.
What does Alydar mean? How many hours does it take to build a deck? Co-authors What does P stand for in simple interest? What does AA stand for in money? A grade assigned to a debt obligation by a rating agency to indicate a very strong capacity to pay interest and repay principal. Such a rating indicates only slightly lower quality than the top rating of AAA. Also called Aa. What is a unit for speed? The SI unit of speed is the metre per second, but the most common unit of speed in everyday usage is the kilometre per hour or, in the US and the UK, miles per hour.
For air and marine travel the knot is commonly used. Actually, this formula comes directly from the proportion calculation -- it's just that one multiplication step has already been done for you, so it's a shortcut to learn the formula and use it. Examples Let's say you rode your bike 2 hours and traveled 24 miles. What is your rate of speed? Your rate is 24 miles divided by 2 hours, so:.
Now let's say you rode your bike at a rate of 10 miles per hour for 4 hours.
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