# college algebra

posted by .

a mason can build a wall in 6 hours less than an apprentice. Together they can build the wall in 4 hours. How long would it take the apprentice to build the wall?

• college algebra -

time for apprentice -- x
time for mason -- x-6

rate of apprentice = 1/x
rate of mason = 1/(x-6)
combined rate = 1l/x + 1/(x-6)
= (2x - 6)/(x(x-6))

then

1/[(2x - 6)/(x(x-6))] = 4
x(x-6)/2x-6) = 4
x^2 - 6x = 8x - 24
x^2 - 14x + 24=0
(x-12)(x-2) = 0
x = 12 or x = 2 , the last makes no sense since x-6 would be negative

so x = 12
the apprentice could build the wall in 12 hours

## Similar Questions

1. ### math

4 men built a wall in 11 days. How long would it take 1 man to build the wall working at the same rate?
2. ### college algebra

'A mason can build a wall in one-half the time it takes an apprentice. Together they build the wall in 12 hours. How long would it take the apprentice working alone to build the wall?
3. ### Algebra

It takes matt 9 hrs longer to build a wall than it takes chris. Working together they can build the wall in 20hrs. how long would it take each working alone to build the wall?
4. ### Math

If 600 bricks measuring 12" by 18" are required to build a wall 10 ft. high (one brick thick), how long is the wall?
5. ### Algebra, URGENT!!!

1) Mio can build a large shed in 15 days less than Yuuko can. If they build it together, it would take them 18 days. How long would it take each of them working alone?
6. ### math

John can build 7 birdhouses in 5 hours, write an equation that will allow john to calculate the time it will take to build any given number of houses. HOW MANY HOUSES in 40 hours?
7. ### Maths proportions

1) Nine milk bottles contain 4.5 litres of milk between them.How much do five bottles hold?
8. ### Math

John can paint a room in 3 hours. His apprentice, working alone, requires 6 hours to do the same job. How long would it take John and his apprentice, working together, to paint the room if they continue to work at the given rates?
9. ### math

If 400 bricks measuring 81" by 31" are required to build a wall 42 ft. high, how long is the wall?
10. ### Maths

a builder needs to calculate the number if bricks needed to build a wall.The wall measure 5m 31cm and each brick measures 16cm.How many bricks are needed to build one layer of the wall?

More Similar Questions