Kary can finish her math final in 3hours. It takes Barry 4 hours to finish the same test. If they work together, how long will it take them to finish the test?

Question

Kary can finish her math final in 3hours. It takes Barry  4 hours to finish the same test. If they work together, how long will it take them to finish the test?

wolf1728 · Answer

If this is the typical "work" problem, the formula is
time1 * time2 / (time1 + time2) = total time
3 * 4 / (3 + 4)
12 / 7
= 1 + 5/7 hours
= 1 hour 42 minutes 51.43 seconds

anonymous · Answer

thank you

wolf1728 · Answer

u r welcome

whpalmer4 · Answer

In general, find the rate of each worker:

Kary does 1 test/3 hours = 1/3 test/hour
Barry does 1 test/4 hours = 1/4 test/hour

together they do 1/3+1/4 test/hour = 4/12 + 3/12 = 7/12 test/hour

1 test * 12/7 hour/test = 12/7 hour

whpalmer4 · Answer

rather than dividing by the fraction, I multiplied by its reciprocal, which is equivalent.

whpalmer4 · Answer

Say they got some guy named Bill who is really fast, and does the test in 2 hours:

Bill = 1 test/2 hours

total rate = 1/2 + 1/3 + 1/4 = 13/12 test/hour

time for the bunch to do the test = 
1 test * 12/13 hour/test = 55.38 minutes