Question

It took a crew 1 h 48 min to row 6 km upstream and back again. If the rate of flow of the stream was 8 km/h, what was the rowing speed of the crew in still water?

Answer 1

d = r*t
upstream:
6 = (v-8)t --> t = 6/(v-8)
downstream:
**Note 1 hr 48 min = 1.8 hr
6 = (v+8)(1.8-t)
Substitute

6 = (v+8)(1.8 - 6/(v-8))
divide by v+8
6/v+8 = 1.8 - 6/v-8
6/v+8 + 6/v-8 = 1.8
combine fractions
6(v-8) +6(v+8) / (v^2-64) = 1.8
6(v-8) +6(v+8) = 1.8(v^2 -64)
12v = 1.8v^2 - 115.2
1.8v^2 -12v -115.2 = 0
use quadratic formula
v = -5.33 or 12
speed must be positive

v = 12