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To solve this problem, we can use a proportion. The problem states that Ms. Hernandez drove \( \frac{3}{10} \) of the total distance in \( \frac{4}{5} \) hours. We need to find how many hours it took her to drive the entire distance to her uncle's house.

Let \( t \) be the total time it takes to drive to her uncle's house. The time taken is directly proportional to the distance driven. Thus, we can set up the following proportion:

\[
\frac{3}{10} \text{ of the distance} = \frac{4}{5} \text{ hours}
\]

\[
\frac{3}{10} \div 1 = \frac{4}{5} \div t
\]

We solve for \( t \) by cross-multiplying:

\[
\frac{3}{10} t = \frac{4}{5}
\]

Now, solve for \( t \):

\[
t = \frac{\frac{4}{5}}{\frac{3}{10}} = \frac{4}{5} \times \frac{10}{3} = \frac{40}{15} = \frac{8}{3}
\]

So, it took her \( \frac{8}{3} \) hours, or approximately 2 hours and 40 minutes, to drive the entire way to her uncle's house.

Would you like further details or have any questions?

Here are five related questions:
1. How do you solve proportions involving fractions?
2. Can this method be applied to any distance-time problem?
3. What if Ms. Hernandez drove \( \frac{1}{2} \) of the way? How would the equation change?
4. How do you convert \( \frac{8}{3} \) hours into minutes?
5. What are some other real-life scenarios where proportions like this can be used?

**Tip:** Always make sure the units you're comparing in a proportion are consistent (e.g., both sides of the proportion should represent the same type of quantity).

It took Ms. Hernandez 4/5 hour to drive 3/10 of the way to her uncle's house. How many hours did it take her to drive to her uncle's house?

Learn how to calculate the total time Ms. Hernandez took to drive to her uncle's house using proportions and fractions. This math problem demonstrates key concepts in proportional reasoning and solving equations with fractions. Suitable for students in Grades 5-7.

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