Packages move 300 feet down a high-speed conveyor belt at a rate of r feet per second.

Question

If the speed of the conveyor belt is increased by 5 feet per second, the packages travel that 300 feet in 3 seconds less time than before. Find r.

Answer 1

Let t₁ = time it takes for the first situation

 

d = 300, v = r, t = t₁ 

 

v = d/t, t = d/v

 

t₁ = 300/r     eq.1

 

If the speed is increased by 5 then v = r+5, d is still 300 and time is decreased so t = t₁ - 3;

 

t = d/v

 

t₁ - 3 = 300/(r+5)   eq.2

 

By substitution, eq. 1 to eq. 2

 

(300/r) - 3 = 300/(r+5)

 

r = 20 ft/s