Question

the diagram shows how Apple's our process for Market. although the second conveyor belt is shorter, an apple spends the same time on each belt because the second belt moves 5 ft /sec slower than the first. Find the speed (in ft/sec) of each belt.first belt. ft/secsecond belt. ft/sec

Answer 1

First belt: 7.5 ft/sec

Second belt: 2.5 ft/sec

Step-by-step explanation:

Let s represent the speed of the 1st belt.

Distance of the 1st belt = 300ft

So time = distance / speed = 300 / s .............Equation 1

Speed of the 2nd belt = (s - 5)

Distance of the 2nd belt = 100 ft

So time = distance / speed = 100 / (s - 5) .........................Equation 2

Since an apple spends the same time on each belt, we can equate both equations for time and solve for s;

`\begin{gathered} (300)/(s)=(100)/(s-5) \\ 300(s-5)=100s \\ 300s-1500=100s \\ 300s-100s=1500 \\ 200s=1500 \\ s=(1500)/(200) \\ s=7.5\text{ ft/sec} \end{gathered}`

Since the speed of the first belt is 7.5ft/sec, we can go ahead and solve for the speed of the 2nd given that it 5ft/sec slower than the 1st;

`\text{ Sp}eed\text{ of the 2nd belt=}7.5-5=2.5\text{ ft/sec}`