A pleasure boat on a river traveled from City A to City C with a stop at City B. On the first part of the trip, the boat traveled at an average speed of 12 miles per hour. From City B to City C the average speed was 13 miles per hour. The entire trip covered 75 miles. How long did the entire trip take if the two parts each took the same number of hours?
Let x be the time it took to travel from City A to City B.
Since the boat traveled at an average speed of 12 miles per hour, the distance from City A to City B is 12x miles.
Since the boat traveled at an average speed of 13 miles per hour from City B to City C, the distance from City B to City C is 13(x) miles.
The entire trip covered 75 miles, so we have the equation 12x + 13(x) = 75.
Combining like terms, we get 25x = 75.
Dividing both sides by 25, we get x = 3.
Since the two parts each took the same number of hours, the entire trip took 3 + 3 = <<3+3=6>>6 hours. Answer: \boxed{6}.
Let's assume the time taken for each part of the trip is x hours.
The distance traveled in the first part of the trip is 12x miles.
The distance traveled in the second part of the trip is 13x miles.
Since the entire trip covered 75 miles, we can express this as an equation:
12x + 13x = 75
Combining like terms, we get:
25x = 75
Dividing both sides by 25, we get:
x = 3
Therefore, each part of the trip took 3 hours.
Since the total time taken for the entire trip is the sum of the time taken for each part, the entire trip took:
3 + 3 = 6 hours
So, the entire trip took 6 hours.
To solve this problem, let's assume that the time taken for each part of the trip is 't' hours.
In the first part of the trip, the boat traveled at an average speed of 12 miles per hour. Therefore, the distance covered in this part can be calculated as:
Distance1 = Speed1 * Time1
Distance1 = 12 * t
In the second part of the trip, the boat traveled at an average speed of 13 miles per hour. Therefore, the distance covered in this part can be calculated as:
Distance2 = Speed2 * Time2
Distance2 = 13 * t
We know that the entire trip covered 75 miles, so the sum of the distances from both parts should be equal to 75 miles:
Distance1 + Distance2 = 75
12t + 13t = 75
25t = 75
t = 75 / 25
t = 3
Therefore, each part of the trip took 3 hours. Since the two parts took the same number of hours, the entire trip took:
Total time = Time1 + Time2
Total time = 3 + 3
Total time = 6 hours
So, the entire trip took 6 hours.