Question 1034987
It took a crew 8 h 32 min to row 8 km upstream and back again.
 If the rate of flow of the stream was 7 km/h, what was the rowing speed of the crew in still water?
:
Let s = rowing speed in still water.
then
(s-7) = effective speed upstream
and
(s+7) = effective speed downstream 
:
Change 8 hrs 32 min to hrs: 8 + 32/60 = 8 + 8/15 hrs = 128/15
:
 write a time equation, time = dist/speed
Time up + time down = 8hr 32 min
{{{8/((s-7))}}} + {{{8/((s+7))}}} = {{{128/15}}}
simplify, divide by 8
{{{1/((s-7))}}} + {{{1/((s+7))}}} = {{{16/15}}}
multiply by 15(s-7)(s+7), cancel the denominators
 15(s+7) + 15(s-7) = (s-7)(s+7)*16
 15s + 105 + 15s - 105 = 16(s^2 - 49)
 30s = 16s^2 - 784
0 = 16s^2 - 30s - 784
simplify, divide by 2
8s^2 - 15s - 392 = 0
you can use the quadratic formula, but this will factor to
(8s+49)(s-8) = 0
the positive solution is all we want here
s = 8 km/hr in still water
:
:
See if that checks out. Find the actual time each way
8/(8-7) = 8 hrs upstream
8/(8+7) = .533 hrs which is 32 min down stream