Question

A town has two sneaker factories, Sneakerheadz and Nukicks. While Nukicks was closed on Sunday, Sneakerheadz made 900 pairs of shoes. On Monday, both Sneakerheadz and Nukicks made shoes for the same amount of time. Sneakerheadz made sneakers at a rate of 300 sneakers per hour and Nukicks at a rate of 480 sneakers per hour. Nukicks made the same number of pairs of shoes on Monday as Sneakerheadz did on both days.

Write and solve an equation in one variable to find out how many hours the Sneaker factories operated on Monday

(Also please show work so i can understand better thanks)

Answer 1

Sneakerheadz produced 900 pairs on Sunday. And on Monday, they produced shoes at a rate of 300 per hour.

Then the total number of pairs produced is:

S(t) = 900 + 300*t

where t represents the number of hours worked on Monday.

We know that Nuckicks only worked on Monday, and the same amount of time as Sneakerheadz, but at a rate of 480 sneakers per hour.

We can write the total number of pairs as:

N(t) = 480*t

Now we know that Nukcicks produced in Monday the sane number of pairs than Sneakerheadz produced in the two days, then we have that:

S(t) = N(t)

900 + 300*t = 480*t

900 = 480*t - 300*t = 180*t

900/180 = t

5 = t

So the factories operated 5 hours on Monday.