Question 1033438

A tourist boat makes trips both upriver and downriver from its mooring. The downriver trip is 36 km each way and takes 8 hours for the round trip. The upriver destination is 60 km away and it takes 10 hours to get there. Find the speed of the boat in still water and the speed of the river.
<pre>Let speed of boat in still water, be S, and speed of river, R
Since it takes 8 hours for round-trip, we get: 
{{{36/(S + R) + 36/(S - R) = 8}}} ------- eq (i)
Also, {{{S - R = 60/10}}}______S – R = 6_____S = 6 + R ------- eq (ii)
{{{36/(6 + R + R) + 36/(6 + R - R) = 8}}} ------- Substituting 6 + R for S in eq (i)
{{{36/(6 + 2R) + 36/6 = 8}}}
{{{36/(6 + 2R) + 6 = 8}}}
{{{36/(6 + 2R) = 8 - 6}}} 
{{{36/(6 + 2R) = 2}}}
2(6 + 2R) = 36 -------- Cross-multiplying
{{{6 + 2R = 36/2}}} ------ Dividing by 2
6 + 2R = 18
2R = 18 – 6
2R = 12
R, or speed of river = {{{12/2}}}, or {{{highlight_green(matrix(1,2, 6, "km/h"))}}}
S = 6 + 6 -------- Substituting 6 for R in eq (ii)
S, or speed of boat, in still water = {{{highlight_green(matrix(1,2, 12, "km/h"))}}}