90. The boat will sink when the weight on it increases beyond 350 kg. There is a hole in it through whichthe water leaks in at the rate of 0.4 kg/s. The weight of the boat is 1200 kg, and the weight of theboatman is 48 kg. The boatman throws out water at the rate of 0.04 kg/s. There are four passengerswhose weights are 42.5 kg, 53.5 kg, 43.5 kg and 54.5 kg. How long will the boat float?(a) 60 hours (b) 80 hours (c) 96 hours (d) 100 hours (e) 120 hours

To find out how long the boat will float, we need to calculate the rate at which the weight on the boat increases and compare it to the maximum weight the boat can handle.

First, let's calculate the total weight on the boat. The weight of the boat is 1200 kg, the weight of the boatman is 48 kg, and the weights of the four passengers are 42.5 kg, 53.5 kg, 43.5 kg, and 54.5 kg.

Total weight on the boat = weight of the boat + weight of the boatman + sum of passenger weights Total weight on the boat = 1200 kg + 48 kg + (42.5 kg + 53.5 kg + 43.5 kg + 54.5 kg) Total weight on the boat = 1200 kg + 48 kg + 194 kg Total weight on the boat = 1442 kg + 194 kg Total weight on the boat = 1636 kg

Next, let's calculate the rate at which water is entering the boat and the rate at which water is being thrown out by the boatman.

Water entering the boat = 0.4 kg/s Water thrown out by the boatman = 0.04 kg/s

To find out how long the boat will float, we need to determine when the weight on the boat reaches the maximum weight it can handle, which is 350 kg.

Weight increase rate = water entering the boat - water thrown out by the boatman Weight increase rate = 0.4 kg/s - 0.04 kg/s Weight increase rate = 0.36 kg/s

Time taken for the weight on the boat to reach 350 kg = (350 kg - 1636 kg) / 0.36 kg/s Time taken for the weight on the boat to reach 350 kg = -1286 kg / 0.36 kg/s Time taken for the weight on the boat to reach 350 kg = 3572.22 s

Finally, let's convert the time to hours.

Time taken for the weight on the boat to reach 350 kg = 3572.22 s / 3600 s/h Time taken for the weight on the boat to reach 350 kg = 0.992 hours

Since the boat will sink when the weight on it increases beyond 350 kg, the boat will float for approximately 0.992 hours.

Therefore, the correct answer is not provided in the options given.