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1. One number is twice another. The sum of the reciprocal is 9/2 . Find the two numbers.

2. A boat travels 30 miles up a river in the same amount of time it takes to travel 50 miles down the same river. If the current is 5 mph, what is the speed of the boat in still water?


1. Let a=1st no. and b=2nd no. One number is twice another means "a=2(b)"..The sum of the reciprocal is 9/2 means "1/a + 1/b = 9/2".. To find the value of b, we substitute eq.1 to eq.2... So, 1/2(b) + 1/b =9/2,.. Solving this,..3/2b = 9/2... 6=18b... b=1/3... Next is the value of a... a=2(b)....a=2(1/3)...a=2/3.. Therefore the two numbers are 1/3 and 2/3. 2.
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2. The equation is " time = distance/rate". The rate upstream is "(r-5 mph)"... The rate downstream is "(r+5)"... It says that the time to travel is the same, So it means " time(up) = time (down)". With these, we can now have a new equation " 30/(r-5) =50/(r+5) "..... Solve: 30r + 150 = 50r - 250... 20r=400...r = 20 mph... Therefore the speed of the boat in still water is 20 mph.
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