Maths help please? (1 Viewer)

[The_Chosen_One]

A machine produces 30 articles in t hours. If the machine were to produce 5 more articles each hour, it would take half an hour less to produce 30 articles. Find t.

 

[Trebla]

A machine produces 30 articles in t hours. If the machine were to produce 5 more articles each hour, it would take half an hour less to produce 30 articles. Find t.

The machine originally produces 30/t articles per hour. If the machine were to to produce 5 more articles per hour we have the rate of 30/t + 5 articles per hour.

It would take 0.5 hours less than t hours to produce 30 articles at this new rate. In other words it takes t - 0.5 hours to produce 30 articles at the new rate. Therefore the new rate is 30 / (t - 0.5) articles per hour.

Now equating the two different expressions of the rates:
30/t + 5= 30 / (t - 0.5)
(30 + 5t)(t - 0.5) = 30t
30t - 15 + 5t² - 5t/2 = 30t
10t² - 5t - 30 = 0
=> 2t² - t - 6 = 0
(2t + 3)(t - 2) = 0
t = -3/2 or 2
but since t > 0 (it is a unit of time), we take t = 2 hours

 

[Timothy.Siu]

hey guys, do some more maths

lol