To solve this problem, let's define the variables and set up equations based on the information provided:

1. Let $p$ represent the distance Peter ran (in kilometers).
2. Mike ran 5 km further than Peter, so the distance Mike ran is $p + 5$.
3. Herb ran twice the distance Peter ran, so the distance Herb ran is $2p$.
4. The total distance ran by the three men is 17 km.

Step-by-Step Solution

1. Set up the equation for the total distance:

   $p + (p + 5) + 2p = 17$

2. Combine like terms:

   $p + p + 5 + 2p = 17$

   $4p + 5 = 17$

3. Solve for $p$:

   Subtract 5 from both sides:

   $4p = 12$

   Divide by 4:

   $p = 3$

   So, Peter ran 3 km.

4. Calculate the distance Mike ran:

   $p + 5 = 3 + 5 = 8 \, \text{km}$

   So, Mike ran 8 km.

5. Find the ratio of the distance Peter ran to the distance Mike ran:

   $\text{Ratio} = \frac{\text{Distance Peter ran}}{\text{Distance Mike ran}} = \frac{p}{p + 5} = \frac{3}{8}$

Conclusion

The ratio of the distance Peter ran to the distance Mike ran is:

$\boxed{3:8}$

Would you like further details on this problem, or do you have any other questions?

Related Questions

1. How would the ratio change if Mike ran 10 km further than Peter?
2. What if Herb ran three times the distance Peter ran? How would this affect the total?
3. How do you solve for different ratios given varying conditions?
4. How can ratios be simplified when both terms are fractions?
5. Can the ratios of distances help in determining their running speeds if time is given?

Tip

When solving word problems involving distances and ratios, always define variables clearly and translate words into mathematical equations to solve systematically.