If a marine radiotelephone receiver uses 75 watts of power and a transmitter uses 325 watts, how long can they both operate before discharging a 50 ampere-hour, 12 volt battery?

To determine how long the marine radiotelephone receiver and transmitter can operate before discharging a 50 ampere-hour (Ah), 12-volt battery, it's important to first calculate the total power consumption of both devices and then relate that to the battery capacity.

The receiver uses 75 watts, and the transmitter uses 325 watts. By adding these two values, we find the total power consumption:

Total Power = Receiver Power + Transmitter Power = 75 watts + 325 watts = 400 watts.

Next, we need to convert the power consumption into amps since the battery capacity is expressed in ampere-hours. To do this, we can use the formula relating watts (P), volts (V), and current (I):

I = P / V.

Substituting in the values we have:

I = 400 watts / 12 volts = approximately 33.33 amperes.

Now we know that the devices consume about 33.33 amperes of current. The next step is to determine how long the battery can sustain this current draw before it is depleted. The battery has a capacity of 50 Ah, so we can use the formula:

Time (hours) = Battery Capacity (Ah) / Current (A).