Gap Unit Concept (Headstart + Catchup)

First
Betty starts saving $30 per month from January. Dave starts saving $45 per month from March. In which month will Betty and Dave have an equal amount of savings?

(Headstart)
Gap Total = Betty = $30 per month x 2 months earlier = $60

(Catchup)
Gap Unit = Dave - Betty = $45 - $30 = $15 per month
Gap Number = $60 / $15 per month = 4 months

Second
Joseph reads 12 pages of a novel each day. His sister reads only 8 pages of the some novel each day but has started reading it 6 days earlier than Joseph. If Joseph began reading on 1st of February, on which date would his sister and he have read the same number of pages?

(Headstart)
Gap Total = Sister = 8 pages each day x 6 days earlier = 48 pages

(Catchup)
Gap Unit = Joseph - Sister = 12 - 8 = 4 pages each day
Gap Number = 48 pages / 4 pages each day = 12 days

1st of February + 12 days - 1 day = 12th of February (ordered range concept)

Third
Machine A prints 18 books per hour. Machine B prints 12 books per hour. How many hours must Machine A operate so that it will print the same number of books as Machine B given that Machine B has started operating 2 hours earlier than Machine A?

(Headstart)
Gap Total = Machine B = 12 books per hour x 2 hours earlier = 24 books

(Catchup)
Gap Unit = Machine A - Machine B = 18 - 12 = 6 books per hour
Gap Number = 24 books / 6 books per hour = 4 hours

Fourth
Patricia and James are selling funfair tickets. Every day, Patricia can sell 20 tickets while James can sell 14 tickets. If James started selling 9 days earlier than Patricia, how many days will Patricia take to sell the same number of tickets as James?

(Headstart)
Gap Unit Total = James = 14 tickets each day x 9 days earlier = 126 tickets

(Catchup)
Gap Unit Value = Patricia - James = 20 - 14 = 6 tickets each day
Gap Unit Number = 126 tickets / 6 tickets each day = 21 days