Question

A postal carrier delivers mail to 20 mailboxes on one side of a long street. Beginning with the first mailbox, the carrrier takes 5 seconds to sort and put the mail in each mailbox, and the mailboxes are 100 feet apart. How fast (in feet per second) must the carrier walk in order to complete delivery to all 20 mailboxes in 10 minutes? Answer in decimal form as a.b (for example, 9.7).

Answer 1

3.8 seconds

Explanation:

Time taken to sort the mail is
`5` seconds

Let time taken to go from one mailbox to the next be
`x`

Distance between the mailboxes is
`100` ft

So, sorting the mail for one mailbox and going to the next will be done in
`(5+x)` 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

`19(5+x)+5=10* 60\\\Rightarrow 19(5+x)=595\\\Rightarrow 5+x=(595)/(19)\\\Rightarrow x=(595)/(19)-5\\\Rightarrow x=(500)/(19)\ \text{s}`

Time taken to go from one mailbox to the other is
`(500)/(19)\ \text{s}`

Speed is given by

`v=(100)/((500)/(19))\\\Rightarrow v=3.8\ \text{ft/s}`

The speed at which the carrier has to move from one mailbox to the next is 3.8 seconds.