What’s the answer? Alvin paddled for 4 hours with a 5-km/h current to reach a campsite. the return trip against the same current took 9 hours. find the speed of the boat in still water?
since distance = speed * time,
4(x+5) = 9(x-5)
now solve for x
To find the speed of the boat in still water, we can set up a system of equations based on the given information.
Let's assume the speed of the boat in still water is represented by 'b' (in km/h).
Given:
Time taken to paddle to the campsite (with current) = 4 hours
Time taken to paddle back (against current) = 9 hours
Current speed = 5 km/h
When paddling with the current, the effective speed of the boat is the sum of the boat's speed in still water and the current speed.
So, the effective speed when paddling for 4 hours with the current = (b + 5) km/h.
When paddling against the current, the effective speed of the boat is the difference between the boat's speed in still water and the current speed.
So, the effective speed when paddling for 9 hours against the current = (b - 5) km/h.
We know that distance = speed × time.
Distance to the campsite = Distance back
(b + 5) × 4 = (b - 5) × 9
Simplifying the equation:
4b + 20 = 9b - 45
Bringing like terms to one side:
9b - 4b = 20 + 45
5b = 65
Solving for 'b':
b = 65 / 5
b = 13
Therefore, the speed of the boat in still water is 13 km/h.
To find the speed of the boat in still water, we can use the concept of relative motion. Let's break down the given information:
Distance = Speed × Time
Let's consider the speed of the boat in still water as 'x' km/h.
The current's speed is given as 5 km/h.
During the journey to the campsite:
Speed of the boat in still water = Speed of the boat (against the current) + Speed of the current
x + 5 km/h
During the return trip:
Speed of the boat in still water = Speed of the boat (with the current) - Speed of the current
x - 5 km/h
We are given that Alvin paddled for 4 hours to reach the campsite and 9 hours to return.
Using the formula for distance:
Distance = Speed × Time
Distance traveled to the campsite = (x + 5 km/h) × 4 hours
Distance traveled on the return trip = (x - 5 km/h) × 9 hours
Since the distances are the same for both trips, we can set up an equation:
(x + 5 km/h) × 4 hours = (x - 5 km/h) × 9 hours
Now, let's solve the equation step by step:
4x + 20 = 9x - 45
20 + 45 = 9x - 4x
65 = 5x
x = 65/5
x = 13
Therefore, the speed of the boat in still water is 13 km/h.