Final answer:
When both the cold and warm water pipes are opened simultaneously, the tank can be filled in 2.4 hours. This is found by adding the reciprocal rates of each pipe (1/4 for the cold and 1/6 for the warm) to get a combined rate of 5/12 of the tank per hour, and then taking the reciprocal of the combined rate.
Step-by-step explanation:
To determine how long it will take to fill the tank when both the cold and warm water pipes are opened simultaneously, we must consider the rate at which each pipe fills the tank on its own. The cold pipe can fill the tank in 4 hours, and the warm water pipe can fill it in 6 hours. To find out how much of the tank each can fill in one hour, we take the reciprocal of their respective times. This gives us a rate of 1/4 for the cold pipe and 1/6 for the warm pipe.
Adding these rates together provides the combined rate at which both pipes can fill the tank: 1/4 + 1/6. To combine these fractions, we find a common denominator, which in this case is 12. The combined rate then becomes 3/12 + 2/12, which simplifies to 5/12 of the tank per hour.
Finally, to find the total time to fill the tank, we take the reciprocal of the combined rate. Thus, the total time to fill the tank with both pipes open is 12/5 hours. Converting this to decimal form gives us 2.4 hours, which corresponds to option B. Therefore, the correct answer is 2.4 hours.