Algebra 2...?

Question

The current of the Wabash River runs 2 miles per hour. It took Marcia and Marion 45 min to paddle a certain distance upstream and 30 min to paddle back with the current. What was their rate of paddling in still water?

Answer 1

let M be the speed of of marcia and Marion

when they travel upstream, their speed is M - 2
when they travel downstrea, their speed is M + 2

It took them 45 minutes to travel upstream and 30 minutes to travel downstream

distance = speed * time

45min = .75hr
30min = .5hr

upstream
d = .75(M - 2)

downstream:
d = .5(M + 2)


.75(M-2) = .5(M + 2)
.75M - 1.5 = .5M + 1
.25M = 2.5
M = 10 mi/hr

Answer 2

Let r be their rate in still water.
Then going upstream their rate will be r(up) = r - 2
And going downstream their rate will be r(down) = r + 2
45 min = 3/4 hours
30 min = 1/2 hours
D = rt:
(r - 2)(3/4) = (r + 2)(1/2)
3(r - 2) = 2(r + 2)
3r - 6 = 2r + 4
r = 10 miles per hour

Answer 3

Let x = rate of paddling in still water
Upstream rate = x-2
Downstream rate =x+2
Time up =45
Time down = 30
Distance up=Distance down
Distance =rate X time
(x-2)45 =(x+2)30
45x - 90 = 30x +60
15x=150
x=10
Rate of paddling in still water is 10mph.

Answer 4

45*R=D
30*(R+2)=D

45*R = 30R+60
15R=60
rate=4 mph