# Thread: Jack & John

1. ## Jack & John

Jack can paint a wall in 3 hours. John can do the same job in 5 hours. How long will it take if they work together?

Let x = time for both to get the job done

(1/3) + (1/5) = 1/x

15x[(1/3) + (1/5)] = 15x(1/x)

5x + 3x = 15

8x = 15

x = 15/8

Yes?

2. ## Re: Jack & John

Originally Posted by harpazo
Jack can paint a wall in 3 hours. John can do the same job in 5 hours. How long will it take if they work together?

Let x = time for both to get the job done

(1/3) + (1/5) = 1/x

15x[(1/3) + (1/5)] = 15x(1/x)

5x + 3x = 15

8x = 15

x = 15/8

Yes?
Yes!!
Some comments:
1. An easier method to solve:
$\displaystyle \frac{1}{3}+\frac{1}{5}=\frac{1}{x}$
$\displaystyle \frac{8}{15} =\frac{1}{x}$
$\displaystyle x=\frac{15}{8}$

(Your method is correct but probably not the most efficient)

2. $\displaystyle \frac{15}{8}$ hours = 1.875 hours = 1 hour 52.5 minutes or 1 hour 52 min 30 sec.

(I always like to express answers to word problems using the language we would normally use. We would never say "it took 15/8 hours" but we would say "it took I hour 52 and a half minutes".)

3. ## Re: Jack & John

Originally Posted by Debsta
Yes!!
Some comments:
1. An easier method to solve:
$\displaystyle \frac{1}{3}+\frac{1}{5}=\frac{1}{x}$
$\displaystyle \frac{8}{15} =\frac{1}{x}$
$\displaystyle x=\frac{15}{8}$

(Your method is correct but probably not the most efficient)

2. $\displaystyle \frac{15}{8}$ hours = 1.875 hours = 1 hour 52.5 minutes or 1 hour 52 min 30 sec.

(I always like to express answers to word problems using the language we would normally use. We would never say "it took 15/8 hours" but we would say "it took I hour 52 and a half minutes".)
Good. Another one for my files.