SOLUTION: a boat traveled 60 mi down river and then returned. the total time for the round trip was 5 hr. the rate of the current was 5 mph. find the rate of the boat in still water

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: a boat traveled 60 mi down river and then returned. the total time for the round trip was 5 hr. the rate of the current was 5 mph. find the rate of the boat in still water      Log On


   

Question 1077395: a boat traveled 60 mi down river and then returned. the total time for the round trip was 5 hr. the rate of the current was 5 mph. find the rate of the boat in still water
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
              SPEED      TIME               DISTANCE
DOWN          r+5        60%2F%28r%2B5%29           60
RETURN        r-5        60%2F%28r-5%29           60
Total                      5


Solve this time sum equation:
60%2F%28r%2B5%29%2B60%2F%28r-5%29=5

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time spent going down river
+5+-+t+ = time spent going up river
Let +r+ = the rate of the boat in still water
+r+%2B+5+ = the rate of the boat going down riover
+r+-+5+ = the rate of the boat going up river
------------------------------------------------
Going down river:
(1) +60+=+%28+r%2B5+%29%2At+
Going up river:
(2) +60+=+%28+r-5+%29%2A%28+5-t+%29+
----------------------------
(1) +t+=+60%2F%28+r%2B5+%29+
and
(2) +60+=+5r+-+25+-+r%2At+%2B+5t+
(2) +60+=+5r+-+25+%2B+t%2A%28+5-r+%29+
Substitute (1) into (2)
(2) +60+=+5r+-+25+%2B+%28+60%2F%28+r%2B5+%29%29%2A%28+5-r+%29+
(2) +85+=+5r+%2B+%28+60%2F%28+r%2B5+%29%29%2A%28+5-r+%29+
Multiply both sides by +r%2B5+
(2) +85%2A%28+r%2B5+%29+=+5r%2A%28+r%2B5+%29+%2B+60%2A%28+5-r+%29+
(2) +85r+%2B+425+=+5r%5E2+%2B+25r+%2B+300+-+60r+
(2) +5r%5E2+-+120r+-+125+=+0+
(2) +r%5E2+-+24r+-+25+=+0+
(2) +%28+r+-+25+%29%2A%28+r+%2B+1+%29+=+0+
+r+=+25+ ( can't use the other solution )
The rate of the boat in still water is 25 mi/hr
-------------------------------------------
check:
(1) +60+=+%28+r%2B5+%29%2At+
(1) +60+=+%28+25%2B5+%29%2At+
(1) +60+=+30t+
(1) +t+=+2+hrs%0D%0Aand%0D%0A%282%29+%7B%7B%7B+60+=+%28+r-5+%29%2A%28+5-t+%29+
(2) +60+=+%28+25-5+%29%2A%28+5-t+%29+
(2) +60+=+20%2A%28+5+-+t+%29+
(2) +3+=+5+-+t+
(2) +t+=+2+ hrs
OK