Solve the problem. Frank can type a report in 3 hours and James takes 4 hours. How long will it take the two of them typing together?

Answer 1

Together It would take them 7 hours.

Answer 2

Solve the problem. Joe has a collection of nickels and dimes that is worth $6.00. If the number of dimes were doubled and the number of nickels were increased by 6, the value of the coins would be $9.90. How many dimes does he have?

Answer 3

Let Frank do a fraction x of the report and James the remaining fraction of
(1-x). The total time for them to finish is the time it takes for whoever finishes last so expressed in hours, it is:

f(x) = Max[3x, 4(1-x)]

We want to minimize this over x. It is not difficult to see that f(x) has its minimum where

3 x = 4 (1-x)

So, x = 4/7 and f(4/7) = 12/7 =

about 1 hour and 43 minutes.

Answer 4

let the number of nickels originally be x
let the number of dimes originally be y
then 5x + 10y = 600 or
x + 2y = 120

new condition:
5(x+6) + 10(2y) = 990
5x + 20y = 960
x + 4y = 192

subtract the two equations
2y = 72
y = 36
back in first
x + 72 = 120
x = 48

so 48 nickels ---> 2.40
and 36 dimes ----> 3.60
total = 6.00

54 nickels = 2.70
72 dimes - 7.20
total = 9.90

Answer 5

Frank --> 1/3 report/hr
James --> 1/4 report /hr

Frank + James --> 4/12 +3/12 = 7/12 report/hr

so together 12/7 hr or about and hour and 43 minutes