How long will these batteries last if the radio has a resistance of 200 ohms

Four 1.50-V AA batteries in series are used to power a transistor radio. If the batteries can move a charge of 240 C, how long will they last if the radio has a resistance of 200 ohms?

I came up with the same formula as Bill but with 133.3 minutes rather than hours:

240 / .03 = 8000

8000s / 60s/m = 133.3minutes = 2.22 hours

Interestingly, the article below (quoting another article!) states:

"The amount of charge that travels through a typical alkaline AA battery is about 5 kC = 5000 C = 1400 mAh. After that charge has flowed, the battery must be discarded or recharged."

If that were true, we'd have

4 * 5000C / .03C/s = 6.67E5 s

= 6.67E5s / 3.6E3s/h = 185 hours

= 7.7 days.
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I think you mean the cells can store a charge of 240 C. Assuming that is for all 4 cells, then you have 6 volts, and the current is 6/200 = 0.03 amps or 0.03 C/s

240 C. / 0.03 C/s = 8000 seconds or 2.2 hours

IF the 240 C is per cell, multiply the final number by 4.

edit, corrected arith, thanks to the other answer.

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