SOLUTION: Joanna took 30 min. to drive her boat upstream to water-ski at her favorite spot. Coming back later that day, at the same boat speed, took her 25 min. If the current in that part o

Question 183868: Joanna took 30 min. to drive her boat upstream to water-ski at her favorite spot. Coming back later that day, at the same boat speed, took her 25 min. If the current in that part of the river is 5 km per hr. What is the average speed of the boat?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Average speed =(Total Distance)/(Total Time)
Let r=speed of the boat in still water
Distance upstream=(r-5)*(1/2) {30 min=1/2 hr}
Distance downstream=(r+5)*(5/12)
Distance Upstream = Distance Downstream, so:
(r-5)(1/2)=(r+5)(5/12) multiply each term by 12
6(r-5)=5(r+5) get rid of parens
6r-30=5r+25 subtract 5r from and add 30 to each side
6r-5r-30+30=5r-5r+25+30 collect like terms
r=55 mph---------------------speed of the boat in still water
Distance Upstream =(50-5)*(1/2)=25 mi
Distance Downstream=(55+5)*(5/12)=25 mi
Total distance=50 mi
Total Time=(5/12)+(6/12)=11/12 hr
Average Speed of Boat =50/(11/12)=54.5 mph
Hope this helps---ptaylor

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