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 ?

Solution(By Examveda Team)

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