To solve this riddle, let's denote Mai's original speed as S (in miles per hour) and her original time to finish the race as T (in hours). We have been given the distance of the race, which is 100 miles.
We have three pieces of information which will lead to three equations.
1. The formula relating speed (S), time (T), and distance (D) is D = S * T. Since the distance D is 100 miles, the original situation gives us the equation:
\[ 100 = S * T \quad \text{(Equation 1)} \]
2. If Mai traveled 5 mph faster, her speed would be S + 5, and she would finish the race in 4 hours. So, for this situation, we again apply the formula for distance:
\[ 100 = (S + 5) * 4 \quad \text{(Equation 2)} \]
3. If Mai traveled 10 mph slower, her speed would be S - 10, and she would finish the race in 10 hours. Using the formula for distance again:
\[ 100 = (S - 10) * 10 \quad \text{(Equation 3)} \]
Now, we solve these equations to find S (original speed) and T (original time).
From Equation 2:
\[ 100 = 4 * (S + 5) \]
\[ 25 = S + 5 \]
\[ S = 25 - 5 \]
\[ S = 20 \text{ mph} \quad \text{(Original Speed)} \]
Now we know Mai's original speed, we substitute S = 20 into Equation 1 to find T:
\[ 100 = 20 * T \]
\[ T = \frac{100}{20} \]
\[ T = 5 \text{ hours} \quad \text{(Original Time)} \]
Just to confirm our answers, let's check Equation 3 with the found value of S:
\[ 100 = (20 - 10) * 10 \]
\[ 100 = 10 * 10 \]
\[ 100 = 100 \]
This confirms the equation holds true with the value of S we found. Mai's original speed was 20 mph, and her original time to finish the race was 5 hours.
