MathProblemSolver101

4, and 3.5

What is 10 times as much as 4.8 and 0.97 and also 51.03?

48

9.7

510.3

Can’t even explain this.

Nice job, TaliaArticula! Not so good at NT myself. Awesome and detailed solution!

A work is completed such that on the nth day from the start n men join the work force. If one men started the work on first day and completed it in a total of 11 days, then find the number of days in which 11 men working together finish the work.

Let m = number of men

Let d = days

Let w = work

1 * 11 = w.

11 * d = w.

d = ?

Obviously, d = 1 :P

P(2,2) R(6,2) Q(6,5)

P’ will stay the same.

Because RQ = 3, a 1/2 dilation means 1.5 length.

Because PR = 4, a 1/2 dilation means 2 length.

Therefore, we have P(2,2) R(4,2) Q(4,3.5)

Two persons A and B together can do a work in 10 days the same work can be

finished in 18 days if A works alone for 12 days and B works alone for 6 days, then

1) The time required for A to finish the work if he work alone is 15 days

2) The time required for B to finish the work if he work alone is 30 days

3) The time required for A to finish the work if he work alone is 20 days

4) The time required for B to finish the work if he work alone is 40 days 

Let a be number of days it takes for person A to finish the work alone.

Let b be number of days it takes for person B to finish the work alone.

Let 1 represent 100% of the job.

We know that 10/a + 10/b = 1. (1)

We also know that 12/a + 6/b = 1. (2)

(1): Multiplying both sides by ab, we have: 10b + 10a = ab (3)

(2): Multiplying both sides by ab, we have: 12b + 6a = ab (4)

(3) = (4): 10b + 10a = 12b + 6a 

Dividing both sides by 2, we have: 5b + 5a = 6b + 3a.

Moving and combining like terms to one side, we have b = 2a (5).

Substituting (5) into (1): 10/a + 10/2a = 1.

Multiplying both sides by a we have 10 + 5 = a.

So a=15.

Thus b = 30.

Person A will take 15 days, person B will take 30 days.

@Guest becajse 3x^2 and 5y do not share a common integer term nor variable. Both of their coefficients are prime, too. This means that they cannot be factored out, and note that + does not define factors. Multiplying does.

That's a bug, then, isn't it?

If 10 men do a piece of work in 92 days how may days will it take 20 men to do it

Let m = number of men

Let d = number of days

Let w = the work

m*d = w

We are given 10 men can do the work in 92 days.... so

10*92 = w. (1)

20 men = 20 * d = w. (2)

(1) = (2)

10*92 = 20*d

92 = 2 * d

d = 46

Overkill but whatever.

Thank you, CPhill! I love your answers too :-)