1. Current of river = 2miles/h. A boat travels 8 miles upstream and back in 3 ho

Question

1. Current of river = 2miles/h. A boat travels 8 miles upstream and back in 3 hours. What is the speed of boat in still water? I know that the answer is 6, logically, but when I tried solving this using formula, I got 6.122. What is the proper formula to solve this problem? 2. A water tank can be filled by an inlet pipe in 8 hours. It takes twice that long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are open? What is the formula; I know that the answer is 16, logically. 3. Find two consecutive even integers, the sum of whose reciprocals is 3/4.

Explanation / Answer

1. let x = rate in still water of the boat... upstream: rate = (x-2) ... distance = 8 ... time = 8/(x-2) downstream: rate = (x+2) ... distance = 8 ... time = 8/(x+2) the total time = 3 = 8/(x-2) + 8/(x+2) 3 = [8(x+2) + 8(x-2)] / x^2 - 4 ... cross multiplying... 3x^2 - 12 = 16x 3x^2 - 16x - 12 = 0 (3x + 2) (x - 6) = 0 thus x = 6 2. inlet: in one hour: 1/8 outlet: in one hour: -1/16 combined: in one hour: 1/8 - 1/16 = 1/16 of the tank thus it will take 16 hours... 3. 1/x + 1/(x+2) = 3/4 [(x+2) + x]/x^2 + 2x = 3/4 4(2x+2) = 3(x^2+2x) 8x + 8 = 3x^2 + 6x 3x^2 - 2x - 8 = 0 (3x + 4)(x - 2) = 0 thus two numbers: 2 & 4.

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