Please help me with this math problem, thank you!?

Question

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 current.

Answer 1

Let s be Kevin's speed, and c the current.

Using the equation for distance/rate = time, we have two equations in s and c -- one for with the current (s+c) and one for against (s-c):

200 / (s - c) = 8 minutes
200 / (s + c) = 4 minutes

Multiply those out to get the variables out of the denominator:

200 = 8s - 8c
200 = 4s + 4c

I'd solve this pair by addition. Double the second equation and add vertically, and then -8c will cancel 8c:

200 = 8s - 8c
400 = 8s + 8c
============
600 = 16s
s = 600/16 = 37.5 m/min

Use either original equation and the now-known value for s, to solve for c:


200 = 8s - 8c
200 = 8(37.5) - 8c
100 = 8c
c = 12.5 m/min

Now use the original equations to check:

s+c = 37.5 + 12.5 = 50m/min, which would cover 200m in 4 min. That's correct.

s-c = 37.5 - 12.5 = 25m/min, which would cover 200m in 8 min. That's also correct.

"meters per minute" is not a common measure, though it is the natural one given the units in the problem.

If meters per second are desired, divide by 60:

s = 37.5m/min = 0.625 m/sec
c = 12.5m/min = 0.2083 m/sec

Answer 2

k - Kevin's speed in meters/minute
c - current's speed in meters/minute

Against the current, k - c, is the net speed.
With the current, k + c, is the net speed.

200meters = (k - c)meter/minute * 8minutes
200meters = (k + c)meter/minute * 4minutes

This gives two equation in two unknowns...
200 = 8(k - c)
200 = 4(k + c)

Simplify by dividing though each equation to reduce factors
25 = k - c
50 = k + c

Add the two equations to get
75 = (k - c) + (k + c)

Collect terms to get
75 = (k + k) + (c - c)

75 = 2k

Simplify to
37.5 = k

Substitute the answer for k into either of the original equations
200 = 8(k - c)
200 = 8(37.5 - c)

Solve for c
200 = (300 - 8c)
8c = 100
c = 12.5

Answer 3

k is Kevin's speed
r is the speed of the river (lakes don't often have currents.)

d = r t (distance = rate (speed) times time)
200 = 8(k - r). . . . against the current
200 = (8/2)(k+r). . with the current

They're both = 200
8k - 8r = 4k + 4 r

Solve for k in terms of r, oor r in terms of k and plug it back into one of the first two equations.

If it make you feel any better, I checked the answer, and it's correct.

Answer 4

2+2(6+9) consistently multiply the 1st till now including 2+12+18 upload 32 then artwork on the backside 0.5 8^2 + 5 artwork on 8^2 sixty 4+5 upload sixty 9 so which you finally finally end up with... 32/sixty 9 positioned into lowest words divide the two aspects by potential of 8 answer is... 4/9

Answer 5

200 meters= (S speed of kevin-C current)* 8 min
200 = (speed of current + current)*4 min


25 (you have to divid 200 by 8)=s-c
50 (200 divided by 4)=s+c
THE 2 C CANCEL OUT SOOO...
75=2s
s=37.5
c=12.5

Answer 6

rate = distance/time
rate upstream = 200/8 = 25m/minute
rate downstream = 200/4 = 50m/minute
Average speed = (25+50)/2 = 37.5 m/minute
Speed of current =50-37.5 = 12.5 m/minute

Answer 7

total distance in the return journey=400m
total time spent=8+4=12min
average speed=400;12=33.33m;minute
let the speedof the current be xm;min and his speed in stationary water be y, then
200;y-x=8
y-x=25...............(1)
and 200;y+x=4
y+x=50........(2_
(2)-(1) gives
2x=25
x=12.5 m;min. ANS

Answer 8

did he have a lifevest on?