While on vacation, Kevin went for a swim in a nearby lake. Swimming against the current, it took him 8 minutes to swim 200 meters. Swimming back to shore with the current took half as long. Find Kevin's average swimming speed and the speed of the lake's cuurent.
Let the speed of the current be y m/min
let Kevin's rate of swimming be x m/min
against the current: 8(x-y) = 200
with the current : 4(x+y) = 200
from the first 8x - 8y = 200 reduced to
x-y = 25
from the second equation x + y = 50
add them: 2x = 75
x = 37.5 m/min
subbing back in the second
y = 12.5
So the lake's current was 12.5 m/min
and his rate of swimming in still water would be 37.5 m/min
I NEED HELP IN CONVERTING 33/50 INTO A DECIMAL
Cheyenne -- please click Post a New Question and ask ask your question.
yoyoyo
To find Kevin's average swimming speed and the speed of the lake's current, we can use the concept of relative speed.
Let's assume Kevin's speed in still water is S and the speed of the lake's current is C.
When Kevin is swimming against the current, his effective speed will be S - C. We are given that it took him 8 minutes to swim 200 meters.
Using the formula:
Distance = Speed × Time
200 = (S - C) × 8
Similarly, when Kevin is swimming with the current, his effective speed will be S + C. We are given that it took him half as long to swim back to shore.
Using the formula again:
200 = (S + C) × (8/2)
Now, we have two equations:
1. 200 = (S - C) × 8
2. 200 = (S + C) × 4
Let's solve these equations to find the values of S (Kevin's average swimming speed) and C (the speed of the lake's current).
Divide equation 2 by 4 to simplify it:
50 = S + C
Now we have two equations:
1. 200 = (S - C) × 8
2. 50 = S + C
We can solve this system of equations either by substitution or elimination method.
Let's use the elimination method to solve the equations:
Multiply equation 2 by 8 to make the coefficients of C in both equations the same:
8 * 50 = 8S + 8C
400 = 8S + 8C
Multiply equation 1 by 4 to make the coefficients of C in both equations the same:
4 * 200 = 32S - 32C
800 = 32S - 32C
Now, let's add both equations together:
400 + 800 = 8S + 8C + 32S - 32C
1200 = 40S - 24C
Simplify the equation:
40S - 24C = 1200
Now, divide both sides of the equation by 8 to simplify it further:
5S - 3C = 150
Now, we have a new equation:
5S - 3C = 150 -- (equation 3)
Let's solve equations 3 and 2 using the elimination method:
Multiply equation 2 by 5 to make the coefficients of S in both equations the same:
5 * 50 = 5S + 5C
250 = 5S + 5C
Subtract equation 3 from equation 2:
250 - (5S - 3C) = 150
Simplify the equation:
250 - 5S + 3C = 150
Rearrange the terms:
-5S + 3C = -100 -- (equation 4)
Now we have equations 3 and 4:
5S - 3C = 150 -- (equation 3)
-5S + 3C = -100 -- (equation 4)
Let's add these equations together:
(5S - 3C) + (-5S + 3C) = 150 - 100
0 = 50
The equation 0 = 50 is not possible and doesn't have a solution. This means there is an inconsistency in the given information, and we cannot determine the average swimming speed (S) or the speed of the lake's current (C) based on the given data.