Two companies working together can clear a parcel of land in 21 hours. Working alone, it would take Company A 10 hours longer

Question

to clear the land than it would Company B. How long would it take Company B to clear the parcel of land alone? (Round your answer to the nearest tenth.)

Answer 1

1/B + 1/31 = 1/21

multiply by 31(21)B

31(21) + 21B = 31B

10B = 651

B = 651/10 = 65.1 hours to complete the work alone for Company B

It's very close to a situation where together they do it in 2 hours

with A alone doing it in 3 hours and B alone doing it in 6 hours

1/6 + 1/3 = 1/2 or divide both sides by 10 to get

1/60 + 1/30 = 1/20

1/65.1 + 1/31 = 1/21 is very similar

You can perhaps see more easily what's going on with simple integers

IF A does 1/6 the job in 1 hour & B does 1/3 the job in 1 hour, Together they do 1/6+1/3 = 1/2 the job in 1 hour