# Distance - Rate - Time – Same Direction 02:33 minutes

**Video Transcript**

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Transcript
**Distance - Rate - Time – Same Direction **

Tom is in big trouble. Two days ago, he pranked his teacher Ms.Trunchbull. Now there is a letter from his teacher waiting in his mailbox at home. He doesn't want his mother to see the letter. So time is ticking.

His mom, working across from the school, finishes work in half an hour, at 3 pm.
Tom has to beat his mom! This is a **Distance-Rate-Time-Problem**. Will he be able to make it?

Tom's school bus leaves school at 2:50 pm. The **distance** between school and mom's work and Tom's home is 12.5 miles. The school bus drives at an **average speed** of 25 miles per hour. His mother is a very fast driver and drives by car at an average of 50 miles per hour.

### Solving Distance-Rate-Time Problems

You know that **rate is distance divided by time**. For example: **miles per hour**. When you are solving distance-rate-time problems, you can use this triangle for help.

- As you can see, it shows that rate,
**"r"**, equals distance,**"d"**over time,**"t"**, because the "d" is on top of the "t". - It also shows you that "t" equals
**"d" over "r"**, because the "d" is on top of the "r". - Lastly, because the "r" and "t" are on the same level, "d" equals "r" times "t".

For this problem you are trying to **solve for time**, "t". So you need to use the **"t" equals "d" over "r" form** of the formula. The time it takes Tom to get home equals the distance, 12.5 miles, divided by the rate, 25 miles per hour,

You can reduce this to 1 over 2. This means, it takes Tom half an hour to get home. So let's calculate how long it takes Tom's mom to drive home. You again need the formula time is distance over rate. She drives 50 miles per hour to get home.

The distance is the same as in the previous **calculation**. To solve for t, you should divide 12.5 by 50. You can reduce this to one fourth. So it will take Tom's mom 15 minutes to get home.

Since Tom leaves school at 2:50 pm and it takes him half an hour to get home, he should arrive home at 3:20 pm. Tom's mom leaves work 10 minutes later at 3:00, this means that she will get home at 3:15. Oh no! Tom's mom is going to beat Tom by 5 minutes!

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