Two hoses, a and b, are used to fill a fish tank with water. hose a puts water into the tank twice as fast as hose b. if both hoses are used, the tank is filled five minutes faster than if just hose a is used. how many minutes would it take for hose b to fill the tank on its own?

Let $A$ be the rate that hose $A$ pumps water. From the given information, hose $B$ pumps water at a rate of $.5A$. Then, let $V$ equal the volume of the tank, and $t$ equal the time for hose $A$ to fill the tank on its own. The volume filled will be equal to the rate multiplied by the time, so we can set up two equations: \begin{align*}

V&=t(A)\\

V&=(t-5)(A+.5A)

\end{align*}The first represents the tank filled by just hose $A$, and the second represents the tank filled 5 minutes faster by both hoses. Setting the two equations equal to each other, we can solve for $t$ as shown: \begin{align*}

(t-5)(A+.5A)&=t(A)\\

\Rightarrow\qquad (t-5)(1.5A)&=tA\\

\Rightarrow\qquad 1.5(t-5)&=t\\

\Rightarrow\qquad 1.5t-7.5&=t\\

\Rightarrow\qquad .5t&=7.5\\

\Rightarrow\qquad t&=15

\end{align*}So, it would take 15 minutes for hose $A$ to fill the tank alone. Since hose $B$ is half as fast, it would take $\boxed{30}$ minutes for hose $B$ to fill the tank on its own.

this story was prepared by jim

mccullaugh in los angeles and

al stewart in new york.

new york the colossal success of "top gun" appears to have dramatically altered madison avenue's

perception of corporate sponsorship

of home video projects.

the paramount home video re- lease, featuring a 60- second diet

pepsi spot, was by no means the

first prerecorded video to carry an advertiser's plug, but it was the

first major theatrical release to do so. in the aftermath of the title's

success, paramount is widely ex- pected to ink a similar deal for

"crocodile dundee" or "star trek

iv" or both.

corporate america's new attraccds push british

recording sales

to 19% gain

london fueled by the compact

disk boom, the value of u.k. manu- facturer shipments of recordings

rose 19% in the 12 -month period ended march 1987, according to the

british phonographic industry.

total value of u.k. shipments for

the period was $755 million for all

configurations. (all value figures

are based on an exchange rate of

$1.68 to the pound sterling.)

cd sales totaled 10.7 million units

worth $121.3 million- compared

with 3.7 million units worth $39.5

million in the prior 12 months -and

accounted for two -thirds of the

overall gain in trade value. at present growth rates, says the bpi, cd

sales for calendar 1987 will reach 20

(continued on page 79)

step-by-step explanation:

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explanation: