# Time / Speed / Distance (MK)

Time Speed Distance problems are a common problem that you find throughout your mathematics education. You may encounter them both in the classroom and in real life and not sometimes not even realize you are. Typically the problems will have you solve for how far you would travel over a period of time at a certain speed. I will go over in this lesson how you can solve for any of the 3 factors in the problem: distance or time or speed. This Mathematics Knowledge skill is basic yet can be challenging for those that are still new to the concepts of time/speed/distance.

As an example, if you travel a distance of 100 miles, and you go at a speed of 50mph, then you already know that it should take you two hours to get there. Also, if a friend comes to visit you from 100 miles away and they tell you that it takes them 4 hours to reach your home, you know that the AVERAGE speed is 25mph. Got it? Lets take a deeper look.

The equation that we work with to solve these is DISTANCE = TIME * SPEED.  The same equation will be used no matter with part you are looking for, just making small adjustments depending on the goal of the word problem.

The key to solving this type of word problems is to figure out EXACTLY what is missing from the problem. Once you know which part is missing, the easier it is to solve for it.

## Solve For Distance

First lets take a look at how to solve word problems when you are trying to solve for the distance travelled. These problems will typically include a speed and a time travelled in the provided information. So by following the base equation ( D=S*T), just need to insert the speed and time and solve the equation.

Example:

Bill drove this car at an average of 50 miles per hour on his way to his parents house. He left his house at noon and arrived 4 hours later. How far is Bill’s parents house from his?

First thing is to extract the information we need to solve the problem.

Find the speed / distance / time:

• Time: 4 hours
• Speed: 50 miles per hour
• Distance: ???

The problem would solve like this:

• DISTANCE = SPEED * TIME
1. Distance = 50mph * 4 hours = (50 *4)
2. Distance = 200 miles

## Solve for Speed

Ok, lets take a look at the same problem but worded a little differently:

Example:

Bill drove to his parents house to visit this weekend. His parents live about 200 miles away and it took him 4 hours to complete the car trip to get to their house.  How fast was Bill driving during this car?

We will repeat the same process, and extract the information we need to solve the problem. Find the speed / distance / time:

• Time: 4 hours
• Speed:  ????
• Distance: 200 miles

When looking for the speed we still use the same equation, but will need to calculate it a bit different:

• DISTANCE = TIME * SPEED
1. 200 miles = 4 hours * X mph     or    200 = 4x
2. Isolate the missing factor by dividing both sides by 4
3. (200/4) = 4x/4
4. 50 = x
5. Average speed is 50 mph.

## Solve for Time

Lastly, we will take a look at how to work out the 3rd variation of the same problem:

Bill drove to his parents house to visit this weekend. His parents live about 200 miles away and he drove an average speed of 50 mph. How long did he take to make the trip?

Repeat the same process of extracting the information we need to solve the problem.

Find the speed / distance / time:

• Time: ???? hours
• Speed: 50 pmh
• Distance: 200 miles

Here is how we solve for the time:

DISTANCE = TIME * SPEED

1.  200 miles = X hours * 50 mph   or   200 = 50x
2. Isolate the missing factor by dividing both sides by 50.
3. (200/50) = (50x / 50)
4. 4 = x
5. Time = 4 hours

## TIME SPEED DISTANCE RECAP

• DISTANCE = TIME * SPEED
• Be sure to figure out EXACTLY what the problem is looking for
• Isolate the missing factor
• Pay attention to the units for each of the factors:
• Speed is shown as  distance/time  (ie  miles per hour, feet per second, etc)
• Distance is a measure of length (ie miles, feet, inches, nautical miles, etc)
• Time will be minutes, hours, seconds, etc

If you have any questions please comment and good luck on your studying for the ASVAB exam!