Can someone please help me with this math extra credit problem? thank you i really appreciate the help.?

Question

The total time available to do a certain job is 3 hours. After one machine has been working on this job for 1 hour, another machine which would have taken half as many hours to do the job alone was brought in. it was put to work with the first machine, and the job was finished exactly on time. How many hours would it have taken the first machine to do the job alone?

Answer 1

rate of first machine = r
rate of second machine = 2*r

complete job = 1

work = rate * time
work performed in first hour = r * 1 = r
work performed in last two hours = (r + 2*r) * 2 = 6r

complete job = work performed
1 = [ r ] + [ 6r ]
1 = 7r
r = 1/7 (rate of first machine)

time = work / rate
=1 / (1/7)
=7 hours

Answer 2

Let x=rate for the 1st machine. total=1*x+2*(x+2x)=7x.
Therefore the ist machine could do the job in 7 hrs. The 2nd machine could do the job in 3.5 hrs.

check
the 1st machine, does 1/7 of the job/hr or 3/7 in 3 hrs. The 2nd machine does 2/7 of the job/hr or 4/7 in 2 hrs.
3/7+4/7=7/7=1

Answer 3

let's work with rates: r1 first machine, r2 second.
r2=2*r1 r1*(1)+(r1+r2)*(2)=1 complete job
7r1=1
r1=1/7 of job per hour if working alone
Answer It would take it 7 hours

A check 1/7 + 2/7 + 4/7 = 1

Answer 4

x + 2y + 2x = done in 3 hours

where
x = machine 1
and
y = machine 2

therefore
3x + 2y = 3 hours (done)

if y = 2x becuse its twice as fast you can substatute
3x + 4x = 3 hours (or done)
or 7x = done.

therefore it would take x 7 hours to finish it alone
or by substatuting the other way(y for x) you can see it takes
3.5 hours for Y to finish it alone.

Answer 5

Good Luck with that. Sorry, No clue.

Answer 6

a million. ax - bx - c = d + bd ax - bx - c + c = d + bd + c ax - bx = d + bd + c ax - bx + bx = d + bd + c + bx ax = d + bd + c + bx ax/x = (d + bd + c + bx)/x a = (d + bd + c + bx)/x 2. a(x + b) = b(x -c) - x a(x + b)/(x + b) = ((b(x-c)-x)/(x + b) a = ((b(x-c)-x)/(x + b)