Answer:
3.8 seconds
Step-by-step explanation:
Time taken to sort the mail is [tex]5[/tex] seconds
Let time taken to go from one mailbox to the next be [tex]x[/tex]
Distance between the mailboxes is [tex]100[/tex] ft
So, sorting the mail for one mailbox and going to the next will be done in [tex](5+x)[/tex] seconds
This will happen 19 times and 5 seconds will be needed to sort the mail for the last mail box. The carrier will have to deliver to all the 20 mailboxes in 10 minutes. So, the total time taken will be
[tex]19(5+x)+5=10\times 60\\\Rightarrow 19(5+x)=595\\\Rightarrow 5+x=\dfrac{595}{19}\\\Rightarrow x=\dfrac{595}{19}-5\\\Rightarrow x=\dfrac{500}{19}\ \text{s}[/tex]
Time taken to go from one mailbox to the other is [tex]\dfrac{500}{19}\ \text{s}[/tex]
Speed is given by
[tex]v=\dfrac{100}{\dfrac{500}{19}}\\\Rightarrow v=3.8\ \text{ft/s}[/tex]
The speed at which the carrier has to move from one mailbox to the next is 3.8 seconds.
