Two pipes are connected to the same tank. when working together, they can fill in 2hrs. the larger pipe, working alone, can fill the tank in 3 hrs less time than the smaller one. how long would the smaller one take, working alone, to fill the tank?

The smaller pipe can fill the tank in 6 hours alone.

Step-by-step explanation:

Let us assume that the smaller pipe can fill the tank alone in x hours and the larger pipe fills it in (x - 3) hours.

Therefore, the smaller pipe in 1 hour can fill part of the tank.

Again the larger pipe in 1 hour can fill part of the tank.

So, if both the pipes are open then, in 1 hour they can fill ( part of the tank.

Therefore, they can fill the full tank in hours.

As per given condition, we can write

⇒ x² - 3x = 4x - 6

⇒ x² - 7x + 6 = 0

⇒ (x - 6)(x - 1) = 0

⇒x = 6 or x = 1

But x can not be less than 2 hours.

So, x = 6 hours.

Therefore, the smaller pipe can fill the tank in 6 hours alone. (Answer)

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

she will sew have sewn five dresses   and be 1/3 done with the sixth one in an hour.

step-by-step explanation:

3/4 of an hour=45 mins

lucy makes 1 dress per 11.25 minutes

45 mins+11.25 mins=56.25 mins

60 mins- 56.25 mins=3.75 mins

3.75 mins is 1/3 of of 11.25 mins

therefore she the other 1/3 would be part of the hour and she will have sewn 5 dresses and begun the sixth.

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