# Word problems

• Oct 7th 2006, 11:07 PM
reiward
Word problems

Jose can do a piece of work in 20 days and his friend can do the same work in 25 days. How long will it take them to finish the work if they will work together?

If the larger of the two numbers which is 36 is divided by the smaller, the quotient is 3 and remainder is 3. What is the smaller number?

The sum of two numbers is 52. If the ratio is 3/10, what are the numbers?
That's all. Thanks!
• Oct 7th 2006, 11:17 PM
CaptainBlack
Quote:

Originally Posted by reiward
Jose can do a piece of work in 20 days and his friend can do the same work in 25 days. How long will it take them to finish the work if they will work together?

Jose does 1/20 of the work per day, his friend does 1/25 of the work per
day. Together they do:

1/20+1/25 = 9/100

of the work per day, so they take 100/9=11.11 days to complete the work
working together.

RonL
• Oct 7th 2006, 11:21 PM
CaptainBlack
Quote:

Originally Posted by reiward
If the larger of the two numbers which is 36 is divided by the smaller, the quotient is 3 and remainder is 3. What is the smaller number?

larger/smaller=3 remainder 3

theis means that

larger = 3*smaller +3

as the larger is 36, we have:

36 = 3*smaller +3,

so subtracting 3 from both sides:

36 - 3 = 33 = 3*smaller + 3 -3 = 3*smaller

so

33 = 3*smaller,

and so smaller = 11.

RonL
• Oct 8th 2006, 04:35 AM
topsquark
Quote:

Originally Posted by reiward
The sum of two numbers is 52. If the ratio is 3/10, what are the numbers?
That's all. Thanks!

Let the two numbers be x and y.

Thus x + y = 52
and
x/y = 3/10

From the second equation we have
10x = 3y

y = (10/3)x

Putting this into the first equation:
x + (10/3)x = 52

(13/3)x = 52

x = (3/13)*52 = 12.

Thus y = (10/3)x = (10/3)*12 = 40.

-Dan
• Oct 8th 2006, 03:23 PM
ThePerfectHacker
Quote:

Originally Posted by reiward

Jose can do a piece of work in 20 days and his friend can do the same work in 25 days. How long will it take them to finish the work if they will work together?

Here is a rule.

If it takes a man "a" amount of time to do a work. And it takes a woman "b" amount of time to do a work. Then it takes,
ab/(a+b)
Amount of time to do it together.
a=25 and b=20
• Oct 8th 2006, 06:27 PM
reiward
Quote:

Originally Posted by CaptainBlack
larger/smaller=3 remainder 3

theis means that

larger = 3*smaller +3

as the larger is 36, we have:

36 = 3*smaller +3,

so subtracting 3 from both sides:

36 - 3 = 33 = 3*smaller + 3 -3 = 3*smaller

so

33 = 3*smaller,

and so smaller = 11.

RonL

thanks, but how did that became "+3".. and why did you subtract 3 from both sides...
• Oct 8th 2006, 06:31 PM
reiward
Quote:

Originally Posted by topsquark
Let the two numbers be x and y.

Thus x + y = 52
and
x/y = 3/10

From the second equation we have
10x = 3y

y = (10/3)x

Putting this into the first equation:
x + (10/3)x = 52

(13/3)x = 52

x = (3/13)*52 = 12.

Thus y = (10/3)x = (10/3)*12 = 40.

-Dan

I cant understand.. How did that become 13/3 and then 3/13.. I knw the answers are correct but I can't understand the solutions...
• Oct 8th 2006, 06:40 PM
Quick
Quote:

Originally Posted by reiward
I cant understand.. How did that become 13/3

Rewrite: 1x+(10/3)x

Rewrite again: (3/3)x+(10/3)x

thus: (13/3)x

Quote:

and then 3/13.. I knw the answers are correct but I can't understand the solutions...

now divide both sides by 13/3 to get: x=52/(13/3)

but remember, to divide you multiply by the inverse of the fraction, thus: x=52*(3/13)
• Oct 8th 2006, 06:53 PM
reiward
Quote:

Originally Posted by Quick

Rewrite: 1x+(10/3)x

Rewrite again: (3/3)x+(10/3)x

thus: (13/3)x

now divide both sides by 13/3 to get: x=52/(13/3)

but remember, to divide you multiply by the inverse of the fraction, thus: x=52*(3/13)

oh i see, thanks! :)
• Oct 8th 2006, 08:26 PM
CaptainBlack
Quote:

Originally Posted by CaptainBlack
larger/smaller=3 remainder 3

theis means that

larger = 3*smaller +3

as the larger is 36, we have:

36 = 3*smaller +3,

so subtracting 3 from both sides:

36 - 3 = 33 = 3*smaller + 3 -3 = 3*smaller

so

33 = 3*smaller,

and so smaller = 11.

RonL

Quote:

Originally Posted by reiward
thanks, but how did that became "+3".. and why did you subtract 3 from both sides...

The +3 is the remainder that you are told exists.

I subtract 3 from both sides as a long winded way of moving the +3 on the
right over to become -3 on the left.

RonL