SOLUTION: Please help me with these word problems... 1. A boat goes 240 miles downstream in the same time it can go 160 miles upstream. The speed of the current is 9 miles per hour. Find

Question 271333: Please help me with these word problems...
1. A boat goes 240 miles downstream in the same time it can go 160 miles upstream. The speed of the current is 9 miles per hour. Find the speed of the boat in still water.
2. To determine the number of fish in a lake, a park ranger catches 200 fish, tags them, and returns them to the lake. Later, 144 fish are caught, and it is found that 40 of them are tagged. Estimate the number of fish in the lake.
3. Frank can type a report in 4 hours and James takes 6 hours. How long will it take the two of them typing together?
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
1)
D=RT
240=(R+9)T DOWNSTREAM TRIP.
T=240/(R+9)
160=(R-9)T UPSTREAM TRIP.
T=160/(R-9)
BECAUSE THE TIMES ARE THE SAME WE SET THE 2 EQUATIONS EQUAL & SOLVE FOR R.
240/(R+9)=160/(R-9) CROSS MULTIPLY
240(R-9)=160(R+9)
240R-2,160=160R+1,440
240R-160R=1,440+2,160
80R=3,600
R=3,600/80
R=45 MPH. IS THE SPEED OF THE BOAT IN STILL WATER.
PROOF:
240(45+9)=160(45-9)
240/54=160/36
4.444=4.444
2)
40/144=200/X
40X=144*200
40X=28,800
X=28,800/40
X=720 ESTIMATED NUMBER OF FISH IN THE LAKE.
3)
4*6/(4+6)
24/10=2.4 HOURS WHEN THEY WORK TOGETHER.

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