Question

I need help!!!!!!!!!

Answer 1

9514 1404 393

Answer:

  2.  15 cents/min

  3.  7/4 gallon/week = 1.75 gal/wk

Step-by-step explanation:

You want to convert the units without changing the rate. You do this by making use of conversion factors. Each conversion factor has a value of 1, but changes the units. (It has a value of 1 because the quantity in the numerator is equal to the quantity in the denominator.)

In general, you know that when the numerator and denominator of a fraction are the same thing, they cancel, leaving a value of 1. When a variable (or unit) is involved, the cancelled variables (or units) simply disappear.

For example, multiplying (9 dollars)×(100 cents)/(1 dollar) gives ...

  $(9\text{ dollar})\times\dfrac{100\text{ cents}}{1\text{ dollar}}=\dfrac{9\times100\times\text{cents}\times\text{dollar}}{1\times\text{ dollar}}=\dfrac{900\text{ cents}}{1}=900\text{ cents}$

The units of "dollar" cancel, leaving cents. Note that we did this by choosing a conversion factor with units we want in the place we want, and units we don't want on the other side of the fraction bar.

__

2) We want cents in the numerator, so our conversion factor will be (100 cents)/(1 dollar). And we want minutes in the denominator, so our other conversion factor will be (1 hour)/(60 minutes). Multiplying by these conversion factors, our rate becomes ...

  $\dfrac{\ 9}{1\text{ hr}}\times\dfrac{100\text{ cents}}{\ 1}\times\dfrac{1\text{ hr}}{60\text{ min}}=\dfrac{9\times100\times1\text{ cents}}{1\times1\times60\text{ min}}\\\\=\dfrac{900}{60}\cdot\dfrac{\text{cents}}{\text{min}}=\boxed{15\text{ cents/min}}$

__

3) We want gallons in the numerator, so that conversion will be done by (1 gal)/(8 pt). We want weeks in the denominator, so the conversion for that is (7 day)/(1 week).

  $\dfrac{2\text{ pt}}{1\text{ day}}\times\dfrac{1\text{ gal}}{8\text{ pt}}\times\dfrac{7\text{ day}}{1\text{ week}}=\dfrac{2\times1\times7}{1\times8\times1}\cdot\dfrac{\text{gal}}{\text{week}}=\boxed{\dfrac{7}{4}\text{ gal/week}}$