Justin paddles his kayak 6 miles upstream in 1,5 hours. he turns around and paddles downstream, the same distance, in only 1 hour. What is the rate in still water and what is the rate of the water's current
let x - rate in still water
y - rate of current
R * T = D
UPS x-y 1.5 6mi
DOWNS x+y 1 6mi
1.5(x-y)=6 ----- 1.5x-1.5y = 6
-1.5[(x+y)=6] -- -1.5x-1.5y = -9
________________
by elimination -3y = -3
method y = 1mph(current)
x+1=6
x=5mph (still water)
To find the rate in still water and the rate of the water's current, we can use the formula:
Rate in still water = (Rate downstream + Rate upstream) / 2
Let's calculate the rates:
Rate upstream = Distance / Time = 6 miles / 1.5 hours = 4 miles per hour
Rate downstream = Distance / Time = 6 miles / 1 hour = 6 miles per hour
Rate in still water = (6 miles per hour + 4 miles per hour) / 2 = 5 miles per hour
To find the rate of the water's current, we can subtract the rate in still water from the rate downstream or upstream:
Rate of the water's current = Rate downstream - Rate in still water = 6 miles per hour - 5 miles per hour = 1 mile per hour
Therefore, the rate in still water is 5 miles per hour and the rate of the water's current is 1 mile per hour.