Two cranes can unload a ship together in 8 hours. The faster crane takes 12 hours less than the slower crane, if each were to unload the same ship alone. How long does it take for each crane to unload this ship?
Fast Crane = A unload x /hour Slow Crane = B unload y /hour A + B = 8 hours x /hour + y /hour = 8 hours (average rate) average rate = (x + y) / 2 so 8 hours = (x + y) / 2 and x + y = 16 since the slow crane is 12 hours longer, x must be 2 hours, since they will both take 2 hours and the slower crane will take 2 hours plus 12 hours equalling 14 hours. The rate of crane A is 2 hours to unload and the rate of crane B is 14 hours to unload. The average rate for both to unload is 8 hours. There were certain assumptions made to solve this puzzle and it is not clear how they actually operate on the ship while unloading. ~~ The most practical way to unload the ship is *NOT* to use the slower crane since it takes longer for them to work combined, than for the faster crane to work alone !! A tricky but fun question !! :-b
I'm surprised by how difficult and convoluted the other answers are. They're also wrong. If two cranes are working together and one crane can, in fact, do the job in two hours, then it cannot possibly take longer than two hours with the help of another crane. That makes no sense just by simple reasoning. So the answer of 2 and 14 hours is not correct. Not even close, really. Here's the simple, neat, and correct approach using basic algebra with no assumptions necessary or made: If crane 1 can unload at a rate1/x per hour, then crane 2 can unload at 1/(x+12) per hour since it takes 12 hours longer. The two cranes combined, unload at 1/8 per hour, which must be faster than either one alone. Example: If I can eat a pie in 3 hours and you can eat a pie in 6 hours: 1/3 + 1/6 = 3/6 = 1/2, so together we can eat a pie in just 2 hours... less time than either one alone. Makes sense. Back to the cranes, then: 1/x + 1/(x+12) = 1/8 (2x+12) / (x^2 + 12x) = 1/8 16x + 96 = x^2 + 12x x^2 - 4x - 96 = 0 (x - 12) (x + 8) = 0 - x = 12 or -8 Since the rate cannot be -8, the answer is x = 12 Crane A can unload all by itself in 12 hours. Crane B can do it in 24 hours, and together they can do it in just 8 hours. Check: 1/12 + 1/24 = 3/24 = 1/8 Their combined rate is, indeed, 1/8 per hour!
If an answer of -4 hours is expected, pl. excuse. The practical difficulties of the faster cranes are constraints - the loading to / unloading from any crane is tricky, time consuming are with practical problems. The ship. yard where it is angered, the type of the cargo also decide the swiftness of unloading ; so it is not simple ratio !
