Earlier this year, I bought my 1st road bike. Its a Royce Union from the 70s with all, of its original components. While everything functions well, I have been having issues with the tires/inner tubes. On a ride a few weeks back, both busted. Today, after buying new tubes, the back tube busted again. What is wrong here? Am I pumping them with too much air? Should I invest in new tires and tubes?

Thanks!