Question 359159
total hours worked: 14.4
time on entering new = n
time on verifying old = p
time on confirming = r
n + p + r = 14.4
{{{2p = n }}} (two times the old)
{{{1(1/2)p = r}}} (one and a half times the old)

substitute for r and n:
{{{2p + p + 1(1/2)p = 14.4}}}

solve for p:
{{{2p + 1p + (3/2)p = 14.4}}}
{{{3p + (3/2)p = 14.4}}}
to add the fraction to the 3p, you must convert 3p to common denominator:
{{{(3/1) x (2/2) = (6/2)}}}
{{{(6/2)p + (3/2)p = 14.14}}}
combine the like terms with the numerators on top:
{{{((6 + 3)/(2))p = 14.4}}}
{{{(9/2)p = 14.4}}}
remove denominator by multiplying both sides by 2:
{{{(2)(9/2)p = 14.4(2)}}}
{{{9p = 28.8}}}
{{{p = 28.8 / 9}}}
{{{p = 3.2 hours}}} 

Now solve for 
{{{2p = n}}}
{{{2(3.2) = n}}}
{{{6.4 = n}}}

Time spent on new reservations = n = 6.4 hours.

Double check your work by finding the r value, time spend confirming:
{{{1(1/2)p = r}}}
{{{1.5p = r}}}
{{{1.5*3.2 = 4.8 = r }}}
Time spent on calling to confirm = r = 4.8 hours.

total time should = 14.4 hours:
r + n + p = 14.4
4.8 + 6.4 + 3.2 = 14.4