Distance Word Problems -Traveling in Different Directions

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: Traveling In Different Directions

Example:
A bus and a car leave the same place and traveled in opposite directions. If the bus is traveling at 50 mph and the car is traveling at 55 mph, in how many hours will they be 210 miles apart?

Solution:
Step 1: Set up a rtd table.

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

If the bus is traveling at 50 mph and the car is traveling at 55 mph, in how many hours will they be 210 miles apart?

Let t = time when they are 210 miles apart.

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

Step 4: Since the total distance is 210, we get the equation:

50t + 55t = 210

105t = 210

Isolate variable t

Answer: They will be 210 miles apart in 2 hours.

The following video gives another example of a distance word problem with vehicles moving in opposite directions.

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