Ports A and B are 400 miles apart. One boat starts from port A for port B at 6:05 and travels with a constant speed of 12 mph. If it leaves port A at 8:20, what speed musta a second boat have to arrive at port B at the same time? Explain your reasoning.
To solve this problem, we need to find the time it takes for the first boat to travel from port A to port B. We'll then use this time to calculate the speed the second boat must have to arrive at the same time.
Given:
Distance between port A and port B = 400 miles
Speed of the first boat = 12 mph
First, let's calculate the time it takes for the first boat to travel from port A to port B. We can use the formula: time = distance / speed.
For the first boat:
Time = 400 miles / 12 mph = 33.33 hours.
Now, let's calculate the time difference between the departure of the two boats. The first boat leaves port A at 6:05 and the second boat leaves port A at 8:20.
Time difference = 8 hours and 20 minutes - 6 hours and 5 minutes
Time difference = 2 hours and 15 minutes = 2.25 hours.
To arrive at port B at the same time, the second boat needs to reach the destination in the same time it took the first boat (33.33 hours), minus the time difference between their departure (2.25 hours).
Therefore, the required time for the second boat to travel from port A to port B is 33.33 hours - 2.25 hours = 31.08 hours.
Finally, we can calculate the required speed of the second boat by using the formula: speed = distance / time.
For the second boat:
Speed = 400 miles / 31.08 hours ≈ 12.86 mph.
Hence, the second boat must have a speed of approximately 12.86 mph to arrive at port B at the same time as the first boat.
To solve this problem, we need to find the speed at which the second boat must travel in order to reach port B at the same time as the first boat. We know that the first boat travels with a constant speed of 12 mph, but we don't know the starting time of the second boat.
Let's break down the problem into two parts:
1. Calculating the time it takes for the first boat to travel from port A to port B:
The distance between ports A and B is 400 miles, and the first boat travels at a speed of 12 mph. We can use the formula: Time = Distance / Speed to calculate the time it takes for the first boat to cover the distance.
Time = 400 miles / 12 mph = 33.33 hours.
2. Calculating the time the second boat needs to travel from port A to port B:
The second boat starts from port A at 8:20, but we don't know its speed. However, we know that both boats should arrive at port B at the same time. Since they both travel the same distance, the time it takes for the second boat to reach port B should be the same as the time it takes for the first boat.
Therefore, the second boat needs to travel the same distance (400 miles) in 33.33 hours. We can use the formula: Speed = Distance / Time to calculate the required speed for the second boat.
Speed = 400 miles / 33.33 hours ≈ 12 mph.
Therefore, the second boat must also travel at a speed of 12 mph in order to arrive at port B at the same time as the first boat.