On Tuesday Philip walked 5/6 hour longer than he did on Monday. On Monday he walked for 1 2/3 hours.
On Monday, Philip walked for 1 2/3 hours, which can be written as 5/3 hours.
On Tuesday, Philip walked 5/6 hour longer than he did on Monday, so he walked for (5/3) + (5/6) hours.
Finding a common denominator for the fractions, (5/3) + (5/6) = (10/6) + (5/6) = 15/6.
Simplifying 15/6, we get 2 3/6, which can be further reduced to 2 1/2 hours.
Therefore, Philip walked for 2 1/2 hours on Tuesday.
To find out how long Philip walked on Tuesday, we need to calculate how much longer he walked compared to Monday and add it to Monday's walking time.
First, let's convert Monday's walking time from a mixed fraction to an improper fraction:
1 2/3 hours = (3*1 + 2)/3 = 5/3 hours.
Now, let's find out how much longer Philip walked on Tuesday compared to Monday's 5/6 hour longer:
5/6 hour longer than 5/3 hours = 5/3 + 5/6 = (10/6 + 5/6) = 15/6 hours.
Next, let's simplify the fraction:
15/6 hours = (3*5)/(2*3) = 5/2 hours.
Therefore, Philip walked for 5/2 hours on Tuesday.