SOLUTION: One roofing crew can finish a 2,800-square-foot roof in 12 hours, and another crew can do the job in 10 hours. If they work together, can they finish before a predict rain in 5 hou

Algebra ->  Rate-of-work-word-problems -> SOLUTION: One roofing crew can finish a 2,800-square-foot roof in 12 hours, and another crew can do the job in 10 hours. If they work together, can they finish before a predict rain in 5 hou      Log On


   

Question 866734: One roofing crew can finish a 2,800-square-foot roof in 12 hours, and another crew can do the job in 10 hours. If they work together, can they finish before a predict rain in 5 hours?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
The rates of each crew are:
1%2F12 and 1%2F10 JOBS per HOUR.

The way uniform rates situations go, R%2Ax=y. In the kind of application for your example, x is time in hours and y is how much or many jobs. The unit of R is jobs per hour and R is a rate. The rate of each crew working together is the sum of their individual rates, so:

1%2F12%2B1%2F10=10%2F120%2B12%2F120=%2810%2B12%29%2F120=22%2F120=highlight%2811%2F60%29 jobs per hour.

Now, if rain will come in 5 hours, will this 5 hours be enough time to do ONE complete job?
highlight_green%28%2811%2F60%29%2A5%3E=1%29 ? Is this true or false?

55%2F60%3E=1 FALSE.
The two crews together will not be able to finish the roof before the rain prediction time.