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 10 miles per hour. From City B to City C the average speed was 15 miles per hour. The entire trip covered 150 miles. How long did the entire trip take if the two parts each took the same number of hours?
Let's assume that it takes x hours to travel from City A to City B. Since the boat travels at an average speed of 10 miles per hour, the distance from City A to City B is 10x miles.
Similarly, the distance from City B to City C is 15(2x) = 30x miles, as the boat travels at an average speed of 15 miles per hour for 2x hours.
The total distance traveled is 10x + 30x = 40x miles, which is equal to 150 miles.
Therefore, 40x = 150.
Simplifying the equation, we get x = 150/40 = 3.75.
Since it takes x hours to travel from City A to City B, the entire trip takes 3.75 + 3.75 = <<3.75+3.75=7.50>>7.50 hours. Answer: \boxed{7.50}.
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 10 miles per hour. Therefore, the distance covered in this part is (10 * t) miles.
In the second part of the trip, the boat traveled from City B to City C at an average speed of 15 miles per hour. Again, the distance covered in this part is (15 * t) miles.
Since the entire trip covered 150 miles, we can set up the equation: (10 * t) + (15 * t) = 150.
Combining like terms, we get: 25t = 150.
Dividing both sides of the equation by 25, we find: t = 6.
So, each part of the trip took 6 hours. Therefore, the entire trip took 6 + 6 = 12 hours.
To solve this problem, we need to set up a system of equations based on the given information.
Let's denote the time it took to travel from City A to City B as "t" hours. Since the boat traveled at an average speed of 10 miles per hour for this portion, the distance covered is 10t miles.
Similarly, let's denote the time it took to travel from City B to City C as "t" hours as well. Since the boat traveled at an average speed of 15 miles per hour for this portion, the distance covered is 15t miles.
According to the problem, the entire trip covered 150 miles. So we can write the equation:
Distance from A to B + Distance from B to C = Total Distance
10t + 15t = 150
Combining like terms, we have:
25t = 150
Dividing both sides of the equation by 25, we get:
t = 6
We now know that both legs of the trip took 6 hours each. To find the total travel time, we simply need to add these two parts together:
Total travel time = Time from A to B + Time from B to C
Total travel time = 6 + 6 = 12
Therefore, the entire trip took 12 hours.