word problemssss........algebra?

Question

5.) three secretaries worked together typing a group of form letters. mellisa could have done them alone in 2 hrs, carol in 3 hrs an linda 2 hrs.how long did the secretaries need to type lettrs working together?
letx=? equation=?

6.) a tank can be filled by two pipes seperately in 10 and 15 minutes respactively. when a third pipe is used simultaneously with the first two pipes, the tank can be filled in 4 minutes. how long would it take for the third pipe alone to fill the tank?
let x=? equation=?

7.) a father is 24 years older than his son. in 8 years he will be twice as old as his son.detrmine their present age
ley_________=son's present age equation=?
_________=father's present age answer=?

8.) lita is fifteen years older than her sister tess.six years ago lita was six times as tess. find their present ages.
let________=present age of tess equation=
_____________=present age of lita

Answer 1

5)Melissa can do work alone in 2 hrs. Therefore she completes 1/2 work in 1hr.
Carol can do 1/3 work in 1hr. and Linda can do 1/2 work in 1 hr.
Therefore,let the work x done by them together in 1 hr.
x = 1/2 + 1/3 + 1/2
x = (3+2+3)/6
x = 8/6
x = 4/3
Hence, they will together whole work in 3/4 hrs meaning 45 mins.


6) A tank can be filled 1/10 in 1 minute by first pipe.
It can be filled 1/15 in 1 minute by second pipe.
Then tank can be filled 1/x in 1 minute
1/4 tanks can be filled in 1 minute by all pipes
Therefore,
1/4 = 1/10 + 1/15 + 1/x
1/4 = (15+10)/150 + 1/x
1/4 = 1/6 + 1/x
1/4 - 1/6 = 1/x
(6-4)/24 = 1/x
1/12 = 1/x
12 = x
Hence, third pipe will take 12mins. to fill the tank.

7) Let the present age of son be x.
Then father's age will be x+24.
In 8 years father's age will be twice of son's
Therefore, when son will x+8 father will be x+32
2(x+8) = x+32
2x +16 = x+32
2x - x = 32-16
x = 16 years.
Son's age is 16 years.
and father's age is 16+24=40years.

8)Let x be the prasent age of tess.
Now lita is x + 15
six years ago tess' age was x - 6
and lita's age was (x+15) - 6 = x + 9
Six years ago Lita was six times as tess.
Hence,
6(x-6) = x + 9
6x - 36 = x + 9
6x - x = 9 + 36
5x = 45
x = 9 years
Therefore, Tess' prsent age is 9 yrs.
and Lita's present age is x + 15 = 9 +15 = 24 yrs.

Answer 2

5. Denote total group of letters as g. Then, melissa's typing speed is sm = g/2, linda's speed is sl = g/2, and carol's speed is sc = g/3. If all three type and need to finish at the same time t then melissa will type t*(g/2) letters, linda t*(g/2), and carol t*(g/3). Therefore:

t*(g/2 + g/2 + g/3) = g and t = 3/4 hour.

From this example we may conclude at the summing of speeds that we will use in the next example.

6. If the tank volume is V then speed of the first pipe s1 = V/10.
speed of the second pipe s2 = V/15, and speed of the third s3 = V/T where T is the time for third pipe to fill a tank. If all three pipes are working they will fill in a tank in time t according to:

t*(V/10 + V/15 + V/T) = V or t*(1/10 + 1/15 * 1/T) = 1

Since t = 4 it follows T = 12 minutes.

7. Denote father's years F and son's S. Follows:

F = S + 24, F + 8 = 2*( S + 8 ). Therefore F = 40, S = 16.

8. L = T + 15, L - 6 = 6*( T - 6 ). Therefore T = 9 and L = 24.

Answer 3

Please note that setting up the correct form and equation initially is important for word problems and keeping track of units is essential:
5.
First, given the following individual typing rate for each sec:
M = 1/2 = 0.5 letter group/hr
C = 1/3 = 0.33 letter group/hr
L = 1/2 = 0.5 letter group/hr
Sum the typing rates to get the collective production rate for the group:
G = 1.33 letter group/hr
and invert to get the time for the group to type one group:
T - (1/1.33) hr/group * 1 group = 0.75 hr or 45 minutes.

6.
This can be solved exactly the same as 5. above, (i.e. compute individual rates, sum to get collective rate, then invert to get collective time):
P1 fill rate = 1 tank/10 min
P2 fill rate = 1 tank/15 min
P3 fill rate = 1 tank/x min
PTot = [ (1/10) + (1/15)+(1/x) ]
Find the commom denom:
Ptot = (15x/150x) + (10x/150x) + (150/150x)
= ( 25x + 150)/150x
= (1 tank/4 min)
Solve for x:
150x/4 = 25x + 150
37.5x = 25x + 150
12.5x = 150
x = 12 min for P3 to fill tank alone

7.
Writing ages,
F = S + 24 (eqn 1)
F + 8 = 2S (eqn 2)
Susbstitute eqn 1 into eqn 2:
S + 24 + 8 = 2S
S = 32 yrs old presently
F = 32 + 24 = 56 yrs old presently

8.
L = T + 15
L - 6 = 6 * (T - 6)
T + 15 - 6 = 6T - 36
T + 9 = 6T - 36
5T = 45
Tess = 9 yrs old presently
Lita = T + 15 = 24 yrs old presently

Answer 4

i aint gonna do it all
it's too long bro!!
anyway i will help u with 5 & 7.
5.
let x be the no of forms to be typed
now mellisa can do it in 2hrs
so her rate is x/2.
and in same way Linda's and carol's rates are x/3 and x/2.
when they do it together let y be the total time
so therefore
x/2*y+x/3*y+x/2*y=x
solve and you get y=3/4.
7.
extremely easy if u kno it do it the rite way
and actually it without all the equations and stuff
juz need to kno the mind games
well, here goes the solution,
let x be sons present age and y be father's present age.
then we gwt, y=24+x.
then it is given after 8 years that father's age becomes double his sons.Then,
y+8=2(x+8).
solve these equations (which is obviously quite easy!!!)
and u get x= 16 and y=40.
now i guess that was some help
the other questions can be done in the same way!!!!!

Answer 5

I was wondering the same thing myself yesterday