We can start solving the problem by using algebra. Let x be the total length of the movie in minutes. Then we know that:
1/3 of the movie is x/3 minutes.
1/5 of the movie is x/5 minutes.
We are told that Joshua watched 1/3 of the movie in the morning and had 1/5 of the movie left to watch at night. Therefore, we can set up the equation:
x/3 + y = x/5, where y is the length of the movie that Joshua watched at night.
We can then solve for y by isolating it on one side:
y = x/5 - x/3
We know that 1/3 + 1/5 = 8/15.
We can simplify by multiplying both sides of the equation by 15:
y = (8/15)*x = 8x/15
We can conclude that Joshua watched 8/15 or approximately 53.33% of the movie at night.