Henry started a trip into the country between 8 am and 9 am when the hand of clock were together, He arrived at his destination between 2 pm and 3 pm when the hands of the clock were exactly 180° apart. How long did he travel ?

Answer: Option A

To be together between 8 am and 9 am, the minute hand has to gain 40 minutes spaces.
55 minutes spaces are gained in 60 minutes.
40 minutes space are gained in $$\left(\frac{60}{55}\times 40\right)$$  minutes = $$\text{43}\frac{7}{11}$$  minutes
So, Henry started his trip at $$\text{43}\frac{7}{11}$$  minutes past 8 am.
Now, to be 180° apart, the hands must be 30 minutes spaces apart.
At 2 pm, they are 10 minutes spaces apart.
∴ The minute hand will have to gain (10 + 30) = 40 minutes spaces.
As calculate above, 40 minutes spaces are gained in $$\text{43}\frac{7}{11}$$  minutes.
So, Henry's trip ended at $$\text{43}\frac{7}{11}$$  minutes past 2 pm
∴ Duration of travel = Duration from $$\text{43}\frac{7}{11}$$  minutes past 8 am to $$\text{43}\frac{7}{11}$$  minutes past 2 pm = 6 hours