Thread: Word problems

Help please. Thanks!

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!

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

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

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

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.
In your example,
a=25 and b=20

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...

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...

Originally Posted by reiward

I cant understand.. How did that become 13/3

You had: x+(10/3)x

Rewrite: 1x+(10/3)x

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

Add: [(3+10)/(3)]x

thus: (13/3)x

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

You had: (13/3)x=52

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)

Originally Posted by Quick

You had: x+(10/3)x

Rewrite: 1x+(10/3)x

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

Add: [(3+10)/(3)]x

thus: (13/3)x


You had: (13/3)x=52

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!

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

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