Math  /  Numbers & Operations

QuestionDebbie rides her bike to school every day. On Monday, she rode 1.5 miles to school in 10 minutes. On her way home, she took a different route through a park, and rode 3 miles in 15 minutes. On which route did Debbie ride at a faster pace? going to school going home
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Studdy Solution

STEP 1

What is this asking? Which bike ride was faster: 1.5 miles in 10 minutes or 3 miles in 15 minutes? Watch out! Don't just compare the distances or times alone; we need to compare the *speeds*!

STEP 2

1. Calculate Speed to School
2. Calculate Speed Back Home
3. Compare Speeds

STEP 3

Let's **define speed**!
Speed is how much distance we cover in a certain amount of time.
We can write it as: Speed=DistanceTime \text{Speed} = \frac{\text{Distance}}{\text{Time}}

STEP 4

To school, Debbie rode 1.51.5 miles in 1010 minutes.
Let's plug those values into our **speed formula**: Speedto school=1.5 miles10 minutes \text{Speed}_{\text{to school}} = \frac{1.5 \text{ miles}}{10 \text{ minutes}}

STEP 5

Now, **calculate the speed**: Speedto school=0.15 miles per minute \text{Speed}_{\text{to school}} = 0.15 \text{ miles per minute} So, Debbie's speed going to school was 0.15\textbf{0.15} miles per minute.
That means she covered 0.15 miles every minute!

STEP 6

Now, let's do the same thing for her ride home!
She rode 33 miles in 1515 minutes.
Using the same **speed formula**: Speedhome=3 miles15 minutes \text{Speed}_{\text{home}} = \frac{3 \text{ miles}}{15 \text{ minutes}}

STEP 7

**Calculate the speed**: Speedhome=0.2 miles per minute \text{Speed}_{\text{home}} = 0.2 \text{ miles per minute} Debbie's speed going home was 0.2\textbf{0.2} miles per minute.

STEP 8

Alright, we have both speeds!
Going to school: 0.150.15 miles per minute.
Going home: 0.20.2 miles per minute.
Which is bigger?

STEP 9

0.20.2 is bigger than 0.150.15!
That means Debbie was riding faster on her way home!

STEP 10

Debbie rode at a faster pace on her way home.

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