https://file.aiquickdraw.com/mathbot/file/1725826612760bn7l2qcw.jpg

The image you've uploaded contains a word problem related to distance, time, and velocity, and provides a quadratic equation. The problem asks you to find the solution for time (t) based on the given equation.

Let's break it down:

**Problem Statement (Paraphrased):**
A car travels a certain distance, first at 25 miles per hour (mph) and then returns over the same distance at 20 mph. The total time for the journey is given as 6.5 hours. You need to determine the time taken for one part of the journey, \( t \). The equation given to solve this is:

\[
\frac{t}{25} + \frac{t}{20} = 6.5
\]

**Options:**
1. \( t = 3.08 \) hours
2. \( t = 3.43 \) and \( t = 3.08 \) hours
3. \( t = 6.51 \) and \( t = 3.08 \) hours
4. \( t = 2.58 \), \( t = 6.52 \), and \( t = 3.08 \) hours

### Step-by-Step Solution:
1. **Write down the equation**: 
   \[
   \frac{t}{25} + \frac{t}{20} = 6.5
   \]

2. **Clear the fractions by multiplying through by the least common denominator (LCD)**:
   The LCD of 25 and 20 is 100. Multiply every term by 100:
   \[
   100\left(\frac{t}{25}\right) + 100\left(\frac{t}{20}\right) = 100(6.5)
   \]

   This simplifies to:
   \[
   4t + 5t = 650
   \]

3. **Combine like terms**:
   \[
   9t = 650
   \]

4. **Solve for \( t \)**:
   \[
   t = \frac{650}{9

A car travels a certain distance, first at 25 mph and then returns over the same distance at 20 mph. The total time for the journey is given as 6.5 hours. Determine the time taken for one part of the journey (t). The equation to solve is: (t / 25) + (t / 20) = 6.5.

Learn how to solve a journey time problem involving a car traveling different speeds over the same distance. This problem uses key algebraic concepts and linear equations, suitable for students in Grades 8-10. Step-by-step instructions provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation