A boat cruises downstream for 2 hours..........?

Question

A boat cruises downstream for 2 hours before heading back. It takes 3.5 hours going upstream to get back. If the speed of the stream is 8 mph, what is the speed of the boat in still water?

Answer 1

let b be the speed of the boat

the resultant speed of the boat when traveling down stream is b + 8. The time is 2hrs

when traveling upstrea, the resultant speed of the boat is b - 8. The time is 3.5 hrs

distance = speed * time

downstream:
d = (b + 8) * 2

upstream:
d = (b - 8) * 3.5

(b + 8)*2 = (b - 8)*3.5
2b + 16 = 3.5b - 28
16 = 1.5b - 28
44 = 1.5b
b = 88/3 mi/hr or about 29.33 mi/hr

Answer 2

Let speed of boat in still water = x mph
Downstream
2 hours
(x + 2) mph
D = 2(x + 8) miles

Upstream
3.5 hours
(x - 8) mph
D = 3.5 (x - 8) miles

2(x + 8) = 3.5 (x - 8)
2x + 16 = 3.5 x - 28
1.5 x = 44
x = 29.3

Speed of boat in still water = 29.3 mph

Answer 3

downstream distance = upstream distance ... ©
(x+8)2 = (x-8)*3.5 .... distance = rate*time
1.5x = 8*5.5
x = 88/3 mph.

Answer 4

(s+8)2 = (s-8)3.5
2s + 16 = 3.5s - 28
16 + 28 = 3.5s - 2s
44 = 1.5s
44/1.5 = s
s = 29.33· mph