Hello!

I'll try the first question.

During the 2 and a half hours when the faster machine has to be shut down, only the slower machine is operating. Within this 2.5 hours, the slower machine produces 75 x 2.5 = 187.5 units.

When both machines can work together, we still have 975 - 187.5 = 787.5 units more to produce.

As mentioned in the question, 1 machine produces 100 units per hour while the other produces 75 per hour. Hence, in 1 hour, with both machines operating, 100 + 75 = 175 units are produced.

So, how many hours are required to produce the remaining 787.5 units? Take 787.5 / 175 = 4.5 hours.

Therefore, the slower machine has to operate for 2.5 + 4.5 = 7 hours, while the faster machine has to operate for 4.5 hours to produce all 975 units.

Hope this helps!