Please show your steps. I am lost on this one.?

Question

Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 4-mph current, it took her 20 minutes longer to get there than to return. How fast will her boat go in still water?

Answer 1

(b+w)t=d downstream
(b-w)t=d upstream

(b+4)t=5
(b-4)(t+20)=5

bt-4t=5
bt-4t+20b-80=5
(subtract these 2 equations)

-20b+80=0
b=4 boat will travel 4mph

Answer 2

To keep the units consistent 20 minutes needs to be expressed as 1/3 hour.

Let
v = velocity of boat in still water

Distance = rate x time

Upstream

5 = (v - 4)(t + 1/3) = (v - 4)t + (1/3)(v - 4)
5 - (1/3)(v - 4) = (v - 4)t
5/(v - 4) - 1/3 = t
t = 5/(v - 4) - 1/3

Downstream
5 = (v + 4)t
5/(v + 4) = t
t = 5/(v + 4)

Set the two equations equal and solve for v.

t = 5/(v - 4) - 1/3 = 5/(v + 4)
3*5(v + 4) - (v - 4)(v + 4) = 3*5(v - 4)
15v + 60 - v² + 16 = 15v - 60
0 = v² - 136
v² = 136
v = √136 = 2√34 ≈ 11.661904 mph

The boat goes 2√34 ≈ 11.661904 mph in still water.

Answer 3

let b be the speed of the boat, because she goes upstream, her resultant speed is b + 4. when she returns, her resultant speed is b - 4

let t be the time she travel upstream, that means t - 1/3 is the time she returns. ( we have to convert minute to hour. 20min = 1/3hr)

the distances are the same

(b + 4)t = 5
(b - 4) (t - 1/3) = 5

now that you have two equations, solve them

Answer 4

Either t must be in hours because velocity is in MPH, or v must be MPM
4 mph = 4/60 mpm = 1/15 mpm

d = v*t for both trips = 5 miles

(v-1/15)*(t + 20) = (v+1/15)*(t)
(vt + 20v -t/15 -20/15) = (vt + t/15)
simplify:
20/15(15v - 1) = 2t/15
10(15v - 1) = (150v - 10) = t

Plug this back into either equation, where you know d = 5 mi
(v+1/15)(150v - 10) = 5 mi
(150v^2 - 10v + 10v - 2/3 ) = 5
150v^2 = 17/3
v^2 = 17/(9*25*2)
v = sqrt(17)/(15sqrt(2)) mi/min
v = 4sqrt(17)/sqrt(2) * sqrt(2)/sqrt(2) = 2*sqrt(34) mph

Answer 5

Let speed in still water be x mph

________Distance___Speed__Time
Upstream------5---------x - 4-----5 / (x - 4)
Downstream--5---------x + 4-----5 / (x + 4)
5/(x - 4) - 5 / (x + 4) = 1 / 3
15.(x + 4) - 15.(x - 4) = (x - 4).(x + 4)
120 = x² - 16
x² = 136
x = 2.√34
Still water speed = 2.√34 mph
Still water speed = 11.7 mph (to 1 dec. place)

Answer 6

let her velocity in still water be xmph
5/(x-4)=1/3+5/(x+4)
15(x+4)=x^2-4+15(x-4)
15x+60=x^2-4+15x-60
x^2=124
x=2sqrt(31). mph

Answer 7

I do not think you can answer that one because you do not know how much the boat went before the current. Sorry if i did not answer your ? i hope this helps. Good Luck!!!