Question

-If A and B are two different numbers selected from the first thirty counting numbers from 1 to 30 inclusive, what is the largest possible value of A+B/ A-B?
-Ann takes medicine for a cold. She must take one pill every 8 hours and a teaspoonful of cough medicine every 5 hours. There are 31 pills. She starts by taking a pill and the cough medicine at the same time. She takes her pills and cough medicine as stated until the 31 pills have been taken. How many times (including the first) will the pill and cough medicine be taken at the same time?

Answer 1

you want the largest possible numerator and the smallest possible denominator:
A=30
B=29
(A+B)/(A-B) = 59

They are taken together every 40 hours.
30*8 = 240 min
In 240/40=6, so they go together 7 times.
(adding in the first pill)

Answer 2

how did you get 40 hours?