High School

It took \( t \) hours for Renaldo to drive from Benton to Carleton. If he had averaged 70 miles per hour, the trip would have taken him \( t - 0.2 \) hours. If he had averaged 60 miles per hour, the trip would have taken him \( t + 0.2 \) hours. The trip distance is the same at either speed, so \( 70(t - 0.2) = 60(t + 0.2) \).

How many hours did it take Renaldo to drive from Benton to Carleton?

Answer :

Using the equation 70(t - 0.2) = 60(t + 0.2) and solving for t, we find that it took Renaldo 2.6 hours to drive from Benton to Carleton.

Renaldo's trip from Benton to Carleton took a certain amount of hours, denoted as t hours. We are given two scenarios with different average speeds and their corresponding times. To find out how long it took Renaldo to drive the distance at the speed he actually drove, we can solve the equation given by setting the distance for each speed scenario equal to each other, since the distance remains constant.

We have the equation 70(t - 0.2) = 60(t + 0.2). Solving for t involves expanding the terms and simplifying:

  1. Multiply through the parentheses: 70t - 14 = 60t + 12
  2. Subtract 60t from both sides: 10t - 14 = 12
  3. Add 14 to both sides: 10t = 26
  4. Divide both sides by 10: t = 2.6 hours

Therefore, it took Renaldo 2.6 hours to drive from Benton to Carleton.

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