Question

Crane A can unload a ship in 10 hours and crane B can unload it in 14 hours. How long will it take the two cranes to unload the ship working together?
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I just need to know how to set this up into an equation.

Answer 1

The key concept here is "find the unit rate". A can unload 1 ship in 10 hours, so its unit rate is 1 ship/10 hours or 0.1 ships/hr. B can unload 1 ship in 14 hours, so its unit rate is 1 ship/14 hours or 0.07142857 ships/hr. A and B working together in perfect harmony ought to be able to unload (1/10 + 1/14) ships per hour.

Answer 2

Here's a similar example. Bob can mow the lawn in 2 hours, Sam can mow the lawn in 3 hours. How long for them to mow it together?

Bob's rate = 1 lawn/2 hours or 1/2
Sam's rate = 1 lawn/3 hours or 1/3

Bob and Sam together mow (1/2 + 1/3) lawns per hour. Make a common denominator to add the fractions:\[\frac{1}{2}*\frac{3}{3} + \frac{1}{3}*\frac{2}{2} = \frac{3}{6}+\frac{2}{6} = \frac{5}{6} \text{ lawns/hr}\]

\(1\text{ lawn}/ (5/6\text{ lawns/hr}) = 1\text{ lawn} * \frac{6\text{ hr}}{5\text{ lawns}} = \frac{6}{5} \text{ hours}\) to mow the 1 lawn working together.

Answer 3

so what's the equation I don't really get anything you just said...

Answer 4

this one?

Answer 5

yeah

Answer 6

I don't really understand what wpalmer was saying

Answer 7

Crane A can unload a ship in 10 hours
crane B can unload it in 14 hours

How long will it take the two cranes to unload the ship working together?

spose a crane works at an even pace; if it takes 10 hours to complete 1 job, how much of the job is completed in 1 hour? in otherwords, what is the hourly rate?

Answer 8

Every hour, crane A unloads 1/10 of the ship. Every hour, crane B unloads 1/14 of the ship. Together, every hour they unload 1/10 + 1/14 of the ship. Add 1/10 + 1/14. Now, divide 1 by that number to give you the number of hours it takes to unload the ship.

Answer 9

so
(1/10 + 1/14)
______________ ?
1

Answer 10

To divide by a fraction, invert it and multiply instead. For example, 1 / (2/3) can be found by multiplying 1 by (3/2).

Answer 11

Close, you want:

\[\frac{ 1} {\frac{1}{10} + \frac{1}{14}}\]

Answer 12

oh but wouldn't that just equal 1/10 + 1/14

Answer 13

Certainly not!

Answer 14

1/10 = 0.1. 1/14 = 0.0714285
Add the two together and you get about 0.17. 1/0.17 does not equal 0.17...

Answer 15

For the purposes of getting a handle on this, say both cranes work at the same speed as crane A. Crane A does 1/10 of the ship each hour. Crane B does 1/10 of the ship each hour. Together, they do 1/10 + 1/10 = 2/10 of the ship per hour. How long would they take to do the entire ship?