a motor boat can travel 45km downstream in 2 hour 30 minutes and 39km upstream in 3 hour 15 minutes. what is the speed of the boat in still water? what is the speed of the current?
b + c = 45 / 2.5 = 18 kph
b - c = 39 / 3.25 = 12 kph
adding equations (to eliminate c)
... 2 b = 30 kph
solve for b
substitute back to find c
To find the speed of the boat in still water and the speed of the current, we'll use the formula:
Speed of the boat in still water = (Speed downstream + Speed upstream) / 2
Speed of the current = (Speed downstream - Speed upstream) / 2
Let's start by converting the time taken to hours and minutes, for easier calculations.
Given:
Distance downstream = 45 km
Time downstream = 2 hours 30 minutes = 2.5 hours (30 minutes = 0.5 hours)
Distance upstream = 39 km
Time upstream = 3 hours 15 minutes = 3.25 hours (15 minutes = 0.25 hours)
Now, let's find the speed downstream:
Speed downstream = Distance downstream / Time downstream
Speed downstream = 45 km / 2.5 hours
Speed downstream = 18 km/hour
Next, let's find the speed upstream:
Speed upstream = Distance upstream / Time upstream
Speed upstream = 39 km / 3.25 hours
Speed upstream = 12 km/hour
Now, we can calculate the speed of the boat in still water:
Speed of the boat in still water = (Speed downstream + Speed upstream) / 2
Speed of the boat in still water = (18 km/hour + 12 km/hour) / 2
Speed of the boat in still water = 30 km/hour / 2
Speed of the boat in still water = 15 km/hour
Finally, let's calculate the speed of the current:
Speed of the current = (Speed downstream - Speed upstream) / 2
Speed of the current = (18 km/hour - 12 km/hour) / 2
Speed of the current = 6 km/hour / 2
Speed of the current = 3 km/hour
Therefore, the speed of the boat in still water is 15 km/hour, and the speed of the current is 3 km/hour.