it takes philip 10 hours to read and cynthia 7 hours. how long will it take if they work together?

Question

round answer two decimal places

Answer 1

The equation to solve is 1/10 + 1/7 = 1/x where x is the number of hours to required to read the entire book if both students are reading it at the same time.

 

By multiplying both sides by 70x we obtain 

 

7x + 10x = 70  which means 17x = 70 which means x = 70/17 or 4.12 as a decimal rounded to the nearest hundredth.

 

However, reading a book is not the type of task that is typically "shared" work. Mowing a lawn is a good example of a task that can easily be shared (provided there is more than one lawn mower available).

Answer 2

Poorly designed question.  Is this how long it takes Cynthia to read a book, and for Philip to read the same book?

 

Reading together? Silently, or aloud? Are they in the same room simultaneously with the one book ?

 

If Cynthia read part of the book for some amount of time, and Philip read the rest of the book for some longer time, would either of them have understood the whole book? Only if reading aloud, and the presence of both would be required, so it would take between 7 & 10 hours--so this is not the ordinary 'work' type of problem.

 

Now, if it were a task that could be shared, such as painting a fence or building a fence, perhaps collaboration would make sense.

 

I'll be very interested in some feedback from your teacher on this misbegotten problem.  Is it a Common Core product?