Wendy begins sanding a kitchen floor by herself and works for 4 hours.

MANHATTAN GMAT OFFICIAL SOLUTION:

You can attack this problem in different ways. No matter what, though, the first thing you should do is focus on the following piece of information:

If Bruce can sand the floor by himself in 20 hours ...

This specifies the rate at which Bruce works in general Note the use of the word can to indicate his general ability. (In the problem scenario, Bruce is not sanding the floor by himself) Bruce's work rate is thus

(1 floor)/(20 hours) = 1/20 floor/hours.

You can also write a quick RTW table and solve for his unknown work rate, but if you can learn to write the work rate directly from statements such as Bruce can sand the floor by himself in 20 hours, then you will save time. Just make sure that you write the units correctly: work rates should always be work per time, not time per work!

As we saw with distance problems, you can lighten your workload by recasting and rephrasing the problem. In this case, you can perform the following arithmetic steps, using only one-row RTW tables at any point. First, focus on the fact that Bruce works alongside Wendy for 2 hours. Since he works at a rate of 1 floor/20 hours, we can set up an RTW chart to figure out how much work Bruce does in those 2 hours:




He is therefore able to complete 2/20, or 1/10, of the floor. This means that Wendy has to do 9/10 of the floor in the 6 hours total that she spends working: 4 hours by herself and 2 hours alongside Bruce.

Now we can solve for her work rate, using another RTW chart:



Finally, take the reciprocal of her work rate to find the time that it takes Wendy to sand one floor. If she can sand 3/20 of a floor in 1 hour, then she will take 20/3 hours to sand 1 floor. You can also use a final RTW chart to find this time:



Answer: C.