Questions: A pleasant boat ride from City A to City C with a stop at City B. On the first part of the trip, from City A to City B, the boat traveled at an average speed of 12 miles per hour. The entire trip covered 100 miles. How long did the entire trip take if the two parts each took the same number of hours?

Solution Steps

To solve this problem, we need to determine the total time taken for the trip. We know the total distance and the speed for the first part of the trip. Since the two parts of the trip took the same amount of time, we can set up an equation to find the time for each part and then sum them up.

1. Let \( t \) be the time taken for each part of the trip.
2. The distance for the first part of the trip is \( 12t \) miles.
3. The distance for the second part of the trip is \( 100 - 12t \) miles.
4. Since the two parts took the same time, we can set up the equation \( 12t = 100 - 12t \).
5. Solve for \( t \) and then calculate the total time.

Let \( t \) be the time taken for each part of the trip in hours. The speed for the first part of the trip is given as \( 12 \) miles per hour, and the total distance of the trip is \( 100 \) miles.

The distance covered in the first part of the trip can be expressed as: \[ \text{Distance}_{\text{first part}} = 12t \] The distance for the second part of the trip is: \[ \text{Distance}_{\text{second part}} = 100 - 12t \] Since both parts of the trip take the same amount of time, we can set up the equation: \[ 12t = 100 - 12t \]

Rearranging the equation gives: \[ 12t + 12t = 100 \] \[ 24t = 100 \] \[ t = \frac{100}{24} = \frac{25}{6} \approx 4.1667 \]

The total time for the trip is: \[ \text{Total Time} = 2t = 2 \times \frac{25}{6} = \frac{50}{6} \approx 8.3333 \]

Final Answer