Someone please help, even if it’s a only

Question

Nick is paddling his canoe along a river with a slow current. He is going to a friend's cottage that is 8 miles away, and then he will paddle back to his starting location.

Because of the current, it takes Nick longer to travel upstream. Let S represent the speed at which Nick paddles the canoe, which is the speed of the canoe would travel if

there were no current

a. Suppose the current is 5 miles per hour downstream. Write an equation for S if it takes Nick 30 minutes longer to paddle upstream versus paddling downstream.

b. Solve the equation in part a for S. Round your answer to the nearest tenth

C.Write and solve an equation to find out how much longer it would take Nick to canoe to his friend's cottage upstream than to paddle back downstream if

Answer 1

half an hour longer upstream than downstream

t+1/2 time upstream, t= time downstream

current = 5 mph,

nick paddles the canoe at "s" mph in still water, for 8 miles and then back

distance =rate of speed times time

d=rt

8 = (s+5)t down stream

8= (s-5)(t+1/2) upstream

solve by substitution elimination

s = about 13.60 mph = speed in still water

8=(s+5)t

t= 8/(s+5)

substitute into the upstream equation

8 = (s-5)(t+1/2) = (s - 5)(8/(s+5)+1/2)

0= (8s-40)/(s+5) + s/2 -5/2-16/2

21/2 = (8s-40)/(s+5) + s/2

21 = (16s-80)/(s+5) +s

21(s+5) = 16s-80 + s(s+5)

21s+5(21) = 16s-80 + s^2 +5s

both linear s terms cancel leaving

s^2 = 105+80= 185

s = sqr185

s = about 13.60 mph in still water

speed downstream = 18.6 mph

speed upstream = 8.6 mph

8/18.6 = .43 hour down stream

8/8.6 = .93 hour upstream

.93-.43 = .5 = 1/2 hour slower downstream