Let the integers be \( x \) and \( x+1 \).
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- Speed = \( \frac{120 \text{ miles}}{3 \text{ hours}} = 40 \text{ mph} \)
- Distance in 7 hours: \( 40 \times 7 = 280 \) miles
- The sum of the squares of two consecutive integers is 145. What is the larger integer?
- Equation: \( x^2 + (x+1)^2 = 145 \)
- Expand: \( x^2 + x^2 + 2x + 1 = 145 \) → \( 2x^2 + 2x + 1 = 145 \)
- Subtract 145: \( 2x^2 + 2x - 144 = 0 \) → divide by 2: \( x^2 + x - 72 = 0 \)
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