Mary Baker rides a bicycle and travels at twice the speed of Wayne Siegert. Mary and Wayne begin a race at the same time and after 5 ​hours, Mary is 25 miles ahead of Wayne.
​a) What is​ Wayne's speed?
​b) What is​ Mary's speed?   Type an integer or a​ decimal

Let's define the speeds of Wayne and Mary:

- Let Wayne's speed be \( x \) miles per hour.
- Since Mary travels at twice the speed of Wayne, her speed is \( 2x \) miles per hour.

Now, according to the problem:
- After 5 hours, Mary is 25 miles ahead of Wayne.

The distance Mary travels in 5 hours is \( 5 \times 2x = 10x \) miles.
The distance Wayne travels in 5 hours is \( 5 \times x = 5x \) miles.

The difference in the distance traveled is 25 miles, so:
\[
10x - 5x = 25
\]
\[
5x = 25
\]
\[
x = 5
\]
Thus, Wayne's speed is 5 miles per hour.

To find Mary's speed:
\[
2x = 2 \times 5 = 10
\]
Mary's speed is 10 miles per hour.

### Answers:
a) Wayne's speed is 5 miles per hour.
b) Mary's speed is 10 miles per hour.

Would you like further details, or do you have any questions?

Here are 5 related questions:
1. How would the solution change if Mary was only 15 miles ahead of Wayne after 5 hours?
2. What if Wayne's speed was 3 miles per hour slower than his current speed?
3. How long would it take for Wayne to finish the race if it was 30 miles long?
4. If Mary and Wayne raced for 7 hours, how far ahead would Mary be?
5. What is the average speed of both racers combined?

**Tip:** Always check units in speed-distance-time problems to ensure accuracy.

Mary Baker rides a bicycle and travels at twice the speed of Wayne Siegert. Mary and Wayne begin a race at the same time and after 5 ​hours, Mary is 25 miles ahead of Wayne. ​a) What is​ Wayne's speed? ​b) What is​ Mary's speed? Type an integer or a​ decimal

Learn how to solve a speed and distance problem involving Mary Baker and Wayne Siegert, where Mary travels twice as fast as Wayne. After 5 hours, Mary is 25 miles ahead of Wayne. This problem demonstrates key algebraic concepts using the speed-distance-time formula. Suitable for students in Grades 6-8.

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