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CBASE: Practice & Study Guide28 chapters | 346 lessons | 20 flashcard sets

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Lesson Transcript

Instructor:
*Julie Zundel*

Julie has taught high school Zoology, Biology, Physical Science and Chem Tech. She has a Bachelor of Science in Biology and a Master of Education.

Knowing how long something takes, how far away something is, and how fast you need to travel, are all important factors in your day. This lesson will give you the tools to calculate time, distance, and velocity in word problems.

Your flight to Hawaii leaves in an hour, and the airport is 30 miles away. How fast do you need to drive in order to catch your flight? A problem like this may sound scary, but this lesson will teach you everything you need to know in order to successfully catch your flight and complete word problems involving time, distance, and velocity.

**Time**, of course, refers to how long something takes and can be measured in a variety of units, such as minutes, hours, and even days. **Distance** measures the space between two places (in this case, you and the airport) and can be measured in units such as centimeters, meters, inches, and miles. Finally, **velocity** is speed with direction, and can be measured in units such as inches per minute or miles per hour. Before we go on, take a look at the table on your screen so you can familiarize yourself with some examples of units associated with distance, time, and velocity.

Distance | Time | Velocity |
---|---|---|

centimeter | millisecond | centimeters per millisecond |

meter | second | meters per second |

inches | minute | inches per minute |

mile | minute | miles per minute |

mile | hour | miles per hour |

As you can see a the smallest level, for example, a centimeter is a measurement of distance, a millisecond is a measurement of time, and centimeters per millisecond is a measurement of velocity. You can see this with all the other measurements in this table, whether it's meters per second or miles per hour. Now that you know what each term means, let's do some word problems!

Let's go back to our Hawaii problem. You don't want to miss the flight, so we'd better figure out how fast you need to go. Specifically, we'll look at the **average velocity**, or the displacement divided by the time. **Displacement** is how far you've traveled from a starting point.

The airport is 30 miles south and you have one hour to get there, so how fast do you need to travel? Remember, velocity is speed and direction, so let's pretend the road to the airport doesn't bend or wind. Start the problem by determining the **variables**, or letters that represent velocity, time, and distance. Let's use *t* for time, *d* for distance, and *v* for velocity.

You know that distance can be measured in miles, so 30 miles must be the distance, and that time can be measured in hours, so 1 hour must be the time. We're trying to figure out the velocity. Set it up to look something like this:

*d*= 30 miles*t*= 1 hour*v*= ?

Now I am going to show you a little trick to solve all of these problems. Take a look at this diagram on screen for the formula.

In order to determine the formula, you need to cover up the variable you are looking for (in this case, *v* or velocity). You can now see we covered up the *v* with a circle.

Build your formula reading from top to bottom, in this case. The formula you are going to use here is: *v* = *d* / *t*. Plug in each variable into the formula and you get:

*v* = 30 miles / 1 hour

Perform the calculation and you get:

*v* = 30 miles per hour

If you want to be napping on the beach, you need to drive at least 30 miles per hour to catch your flight! This problem seemed pretty straightforward and you're probably thinking there isn't any difference between speed and velocity, right?

Let's make this problem a little more challenging. Let's say the road to the airport was 20 miles east and then 10 miles west, and you couldn't have a straight shot because of a mountain. Remember, velocity looks at speed and direction, so this will change things a little.

So to calculate the average velocity, we will need look at the displacement. Here you need to look at how far you actually traveled from your starting point. Start by assigning variables like before:

*t*= 1 hour*v*= ?

Distance is no longer 30 miles. It's 20 miles - 10 miles because we are looking at displacement.

*d*= 10 miles

Now you can solve like before:

*v* = 10 miles per hour

You can see how the direction you are going changes your answer, right? Now this would be a little confusing if you were trying to get to the airport on time, but it's important to see how direction affects your answers for velocity.

Now that you know how to solve for velocity, let's do a problem where we solve for time, or *t*.

While in Hawaii, you planned several activities, but you're afraid you're going to be late for scuba diving since you've gotten held up on your horseback riding adventure. You need to figure out how much longer you will be horseback riding to see if you can make it before your scuba diving boat departs. You have to go three miles west to get back to your car, and your horse is traveling five miles per hour. How much longer until you reach your car?

Just like last time, assign variables to each number. You know 3 is distance in miles. You also know that the distance and displacement rate are the same here because you are going three miles west and not zigzagging. You know the velocity is five miles per hour since miles per hour is a unit associated with velocity. You are trying to find out the time.

*d*= 3 miles*v*= 5 miles per hour*t*= ?

Now use the triangle and cover up *t* to see the formula, referring to the on your screen. Again, build your formula reading from top to bottom.

You can see the formula is *t* = *d* / *v*, so plug in the numbers.

*t* = 3 miles / 5 miles per hour

Perform the calculation and you get:

*t* = 0.6 hours (please note that the 'miles' units cancel out)

So it will take 0.6 hours for you to finish your horseback riding trip. Hopefully your scuba diving boat doesn't leave soon!

The last problem you need to be able to do is solve for distance, or *d*. It's your final day in Hawaii, and you decided to go for a run. Your phone calculated your speed and time but didn't calculate the distance you ran, so you need to do a little math. According to your phone, you ran 0.1 miles per minute and you were gone for 65 minutes. Let's try to figure out how far you went. Assign variables to each number. Oh yeah, and you traveled in a straight line, no zigzagging.

*t*= 65 minutes*v*= 0.1 miles per minute*d*= ?

Use image D to help you determine the formula. Remember, cover up the *d* since that is the variable we are looking for. Now build your formula reading from left to right.

You can see the formula is *d* = *v* x *t* so go ahead and plug in the numbers.

*d* = 0.1 miles per minute x 65 minutes

Perform the calculation and you get:

*d* = 6.5 miles (please note the 'minutes' units cancel out)

So you traveled 6.5 miles. Great job!

Before we finish, let's take a moment to look at the formulas used to solve for time, distance, and velocity. You can memorize these formulas or use the triangle to help you find the formulas. Either way works just fine.

Solving For | Formula |
---|---|

Velocity | v = d / t |

Time | t = d / v |

Distance | d = t x v |

I hope you had a good time in Hawaii and maybe even learned a little about how to calculate time, distance, and velocity problems. Before you board your plane back home, let's take a moment to review. In order to solve word problems for **time**, or how long something takes, which can be measured in a variety of units; **distance**, or the space between two places; and **velocity**, which looks at speed and direction, you need to start by identifying which number in the word problem goes with which variable (*t* for time, *d* for distance, or *v* for velocity). Next use the triangle and cover up which variable you're looking for. If you don't like the triangle, go ahead and memorize the formulas for time, distance, and velocity.

Solving For | Formula |
---|---|

Velocity | v = d / t |

Time | t = d / v |

Distance | d = t x v |

Remember, with velocity you need to take the **displacement** into account. In other words, if your distance isn't a straight line, you have to determine how far you are from the starting point. Once you've figured out the variables and the formula, plug the numbers into the formula, cross off units if need be and, voila, you are done! Okay, okay, I'll let you get going. Remember, you have a flight to catch!

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CBASE: Practice & Study Guide28 chapters | 346 lessons | 20 flashcard sets

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