Question 30688
the solution by the other tutor is wrong.


Let T = time to finish
let P = number of problems
let H = number of hours of study


we are told 2 things:


T varies directly as P
and 
T varies indirectly as H


Mathematically we have T proportinal to {{{ P/H }}}, and hence 


{{{ T = (kP)/H }}} where k is the constant of proportionality


So first we need to find the value of k, for which the question should supply all other variables:


{{{ 2 = (50k)/3 }}}
--> 50k = 6
--> k = 6/50
--> k = 3/25


So, the formula is {{{ T = (3P)/(25H) }}} 


Now we can find the unknown, given the 2 values quoted.


{{{ T = (3*75)/(25*4) }}}
{{{ T = (225)/(100) }}}
--> T = 2.25 Hours

or T = 2 hours 15 minutes


jon.