 # Distance Word Problems - Given the Total Time

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Distance problems are word problems that involve the distance an object will travel at a certain average rate for a given period of time.

The formula for distance problems is: distance = rate × time or d = r × t.

Things to watch out for:
Make sure that you change the units when necessary. For example, if the rate is given in miles per hour and the time is given in minutes then change the units appropriately.

It would be helpful to use a table to organize the information for distance problems. A table helps you to think about one number at a time instead being confused by the question.

### Distance Problems: Given Total Time

Example:
John took a drive to town at an average rate of 40 mph. In the evening, he drove back at 30 mph. If he spent a total of 7 hours traveling, what is the distance traveled by John?

Solution:
Step 1: Set up a rtd table.

 r t d Case 1 Case 2

Step 2: Fill in the table with information given in the question.

John took a drive to town at an average rate of 40 mph. In the evening, he drove back at 30 mph. If he spent a total of 7 hours traveling, what is the distance traveled by John?

Let t = time to travel to town.

7t = time to return from town.

 r t d Case 1 40 t Case 2 30 7 – t

Step 3: Fill in the values for d using the formula d = rt

 r t d Case 1 40 t 40t Case 2 30 7 – t 30(7 – t)

Step 4: Since the distances traveled in both cases are the same, we get the equation:

40t = 30(7 – t)
Use distributive property
40t = 210 – 30t
Isolate variable t
40t + 30t = 210
70t = 210 Step 5: The distance traveled by John to town is

40t = 120
The distance traveled by John to go back is also 120
So, the total distance traveled by John is 240

Answer: The distance traveled by John is 240 miles.

Distance, Rate, Time Word Problems
Two examples of distance, rate, and time. One involves adding the distances in our chart, where as the other example involves setting the distances equal to each other.
Example:
(1) Two truck drivers leave a cafe at the same time, traveling in opposite directions. On truck goes 7 mph faster than the other one. After 4 hr, they are 404 miles apart. How fast is each truck going?
(2) Ryan left the science museum and drove south at a rate of 28 km/h. Jenna left three hours later driving 42 km/h faster in an effort to catch up to him. How long did Jenna have to travel to catch up with Ryan?
Distance-time word problem where the total time is given
Example:
Gordon rode his bike at 15 mph to go get his car. He then drove back at 45 mph. If the entire trip took him 8 hours, how far was his car?

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