A ferry, when empty, travels twice as fast as when it is full. It travels 30 miles south with cargo, spends 30 minutes unloading, and returns to its original port empty in a total of 8 hours. What is the speed of the ferry when it is empty?

Question: A ferry, when empty, travels twice as fast as when it is full. It travels 30 miles south with cargo, spends 30 minutes unloading, and returns to its original port empty in a total of 8 hours. What is the speed of the ferry when it is empty?

Solution:
Let the speed of the ferry when it is full = x mile/h
And, the speed of the ferry when it is empty = 2x mile/h

∴ (30/x) + (30/2x) = 8 - (30/60)
⇒ (60 + 30)/2x = 15/2
⇒ 90/x = 15
⇒ x = 90/15
⇒ x = 6

∴ The speed of the ferry when it is empty = 2 × 6 = 12 mile/h