Question 1058306
{{{x}}}= number of hours the faster computer needs to do the whole job by itself
{{{x+16}}}= number of hours the slower computer needs to do the whole job by itself
{{{1/x}}}= fraction of the task done by the faster computer in one hour
{{{1/(x+16)}}}= fraction of the task done by the slower computer in one hour
We know that the task was completed with work from both computers,
with the slower computer working during
{{{1+14=15}}} hours,
and the faster computer working for one hour.
So, our equation is
{{{1/x+15/(x+16)=1}}}
Multiplying both sides of the equal sign times {{{x*(x+16)}}} we eliminate denominators to get
{{{x+16+15x=x(x+16)}}}
{{{16x+16=x^2+16x}}}
{{{16=x^2}}}
So, {{{x=4}}}= number of hours that the faster computer needs to do the whole job by by itself;
{{{x+16=20}}}= number of hours that the slower computer needs to do the whole job by itself,
meaning that the faster computer is {{{20/4=5}}} times faster.
If we interpret the question as asking for the time it takes the faster computer to run the program working by itself from start to end,
the answer is {{{highlight(4hours)}}} .

NOTE:
Sometimes the question meant does not agree with our interpretation,
and we are puzzled by the answer that is considered the correct answer.
If they meant how long would have taken the faster computer to finish the job after the two computers worked together for 1 hour,
that would be {{{14 hours/5=2.8hous=2hours}}}{{{and}}}{{{48 minutes}}} .