Answer:
The speed of the faster ship is 22.5 m/s
Step-by-step explanation:
The length of the ships are;
Ship 1 = 200 m
Ship 2 = 100 m
The time it takes for the ships to completely cross each other when travelling in opposite directions = 10 seconds
The time it takes both ships to cross each other when travelling in the same direction = 25 seconds
Let x represent the speed of the first ship, ship 1, and y represent the speed of the second ship, ship, 2, we have;
(x + y) × 10 = 200 + 100 = 300
10·x + 10·y = 300...(1)
(x - y) × 20 = 200 + 100 = 300
20·x - 20·y = 300...(2)
Multiply equation (1) by 2, to get;
(x + y) × 10 × 2 = 300 × 2
20·x + 20·y = 600...(3)
Adding equation (1) to equation (3) gives;
20·x + 20·y + 20·x - 20·y = 600 + 300
40·x = 900
x = 900/40 = 22.5
x = 22.5
The speed of the first ship, ship 1 = x = 22.5 m/s
From equation (1), we have;
10·x + 10·y = 300
y = (300 - 10·x)/10 = (300 - 10×22.5)/10 = 7.5
y = 7.5
The speed of the second ship, ship 2 = y = 7.5 m/s
Therefore, the faster ship is ship 1 with a speed of 22.5 m/s