Question

Lindsey rows a boat downstream for 80 miles. The retum trip upstream took 12 hours longer. If the current flows at 3 mph, how fast does Lindsey row in still water?

Answer 1

Answer:

14hrs

Step-by-step explanation:

v = speed in still water

 

t = downstream trip time

 

d = distance = 182 miles; same distance both downstream and upstream

 

t + 12 = upstream return trip time

 

u = current flow = 3 mph

 

Downstream:  d = (v + u)t;  Upstream:  d = (v - u)(t + 12)

 

(v - 3)(t + 12) = 182  (equation 1)

(v + 3)t = 182  (equation 2)

 

Subtract equation 2 from equation 1 to get t:

 

(vt + 12v -3t -36) - (vt + 3t) = 0

 

12v - 6t - 36 = 0

 

t = 2v - 6

 

Substitute this result for t into equation 2 and solve for v:

 

(v + 3)(2v - 6) = 182

 

2v^2 - 6v + 6v - 18 = 182

 

v^2 = 100

 

v = 10 mph

 

t = 2v - 6 = [2(10) - 6] hrs = 14 hrs