A pipe can fill a tank in 6 hours, and another pipe can fill the same tank in 8 hours. If both pipes are opened at the same time, how long (in hours, rounded off to one decimal place) will it take to fill the tank?

Correct option is C

Given:

Pipe 1 fills the tank in 6 hours

Pipe 2 fills the tank in 8 hours

Solution: 

Pipe 1 rate = $$\frac 1 6$$​ 

Pipe 2 rate = $$\frac 1 8$$​​

Combined rate = $$\frac{1}{6} + \frac{1}{8}$$​​

​$$= \frac{4}{24} + \frac{3}{24}$$​​

​$$= \frac{7}{24} \text{ tanks/hour}$$​​

Time to fill tank = $$\frac{24}{7} \text{ hours}$$​​

​$$\approx 3.4 \text{ hours}$$

Alternate Solution: 

LCM of 6 and 8 = 24 hours

Work done by pipe 1 in 24 hours = $$\frac{24}{6}$$​= 4 tanks

Work done by pipe 2 in 24 hours = $$\frac{24}{8}$$​ = 3 tanks

Total work done in 24 hours = 4 + 3 = 7 tanks

Time to fill 1 tank =$$\frac{24}{7}$$​ hours

​$$\approx 3.4 \text{ hours}$$​​