In a swimming race, you find that a swimmer can swim downstream (with the current) in a river, 2 miles in 40 minutes, & upstream (against the current) 2 miles in 60 minutes. How long would it take the swimmer to swim a mile in still water?
40 min = 2/3 hr
60 min = 1 hr
let the speed of the swimmer in still water be x mph
let the speed of the river be y mph
(2/3)(x+y) = 2
2(x+y) = 6
x + y = 3
1(x-y) = 2
x - y = 2
add them
2x = 5
x = 2.5 , then by mental math, y = .3
his rate in still water is 2.5 miles in 60 minutes
so to do one mile would take 60/2.5 or 24 minutes
To find out how long it would take the swimmer to swim a mile in still water, we need to first understand the concept of relative speed.
When swimming downstream, the swimmer benefits from the current, which adds to their speed. On the other hand, when swimming upstream, the current opposes their progress, reducing their effective speed.
Let's use the following variables to solve the problem:
- D: distance
- T: time
- R: rate or speed
Let's calculate the rate (R) of the swimmer in still water.
Since the swimmer swims downstream at a speed of 2 miles in 40 minutes, we can calculate their speed downstream (Rd) as follows:
Rd = D/T = 2 miles / 40 minutes = 1/20 miles per minute
Similarly, since the swimmer swims upstream at a speed of 2 miles in 60 minutes, we can calculate their speed upstream (Ru) as:
Ru = D/T = 2 miles / 60 minutes = 1/30 miles per minute
The speed of the swimmer in still water (Rs) can be calculated by taking the average of the upstream and downstream speeds:
Rs = (Rd + Ru) / 2 = (1/20 + 1/30) / 2 = 1/24
Now that we have the speed of the swimmer in still water, we can determine how long it would take them to swim a mile.
Let's calculate the time (T) required to swim 1 mile:
T = D/Rs = 1 mile / (1/24) = 24 minutes
Therefore, it would take the swimmer 24 minutes to swim a mile in still water.