<PRE><B>Question 67295</B>
The current in the river flowed at 3 miles per hour. The boat could travel 24 miles downstream in one-half the time it took to travel 12 miles upstream. What was the speed of the boat in still water?
:
Let s = speed in still water
:
Speed upstream: (s-3)
Speed downstream: (2+3)
:
Write a time equation: time = dist/speed
:
Time 24 mi downstream = half the time 12 mi upstream
{{{24/((s+3))}}} = {{{.5(12/((s-3)))}}}
:
{{{24/((s+3))}}} = {{{6/((s-3))}}}
:
Cross multiply:
24(s-3) = 6(s+3)
24s - 72 = 6s + 18
24s - 6s = 18 + 72
18s = 90
s = 90/18
s = 5 mph in still water
:
:
Check:
24/8 = 3hr for 24 mi downstream
12/2 = 6hr for 12 mi upstream</PRE>