Question

A factory manufacturers a metal piece in 32 minutes l. New technology allowed the factory to cut that time by 8%. Then another improvement cut the time by 5%. How long does it take to manufacture the piece now?

Answer 1

27.968 minutes

Explanation:

let x be the original time it takes to make the piece. Given production time was cut down in two phases by 8% and 5%, the new time of the piece is calculated as:

`t_0=x\\\\t_1=t_0*(1-r_1),r_1=8\%\\\\t_1=t_0(1-0.08)\\\\t_1=0.92t_0\\\\t_2=t_1*(1-r_2),r_2=5\%\\\\t_2=0.92t_0(1-0.05)\\\\t_2=0.92t_0*0.95=0.874t_0`

We therefore substitute the initial time in the equation:

`t_2=0.874t_0\\\\=0.874*32 \ min\\\\=27.968 \ min`

Hence, it now takes 27.968 minutes to manufacture the piece.