Pool

If water flows into the pool by two inlets, fill the whole for 19 hours. The first inlet filled pool 5 hour longer than the second. How long pool take to fill with two inlets separately?

Correct result:

t1 =  40.66 h
t2 =  35.66 h

Solution:

1t1+1t2=119 t2=t15 1/t1+1/(t15)=1/19  19(x5)+19x=(x5)x  19 (x5)+19 x=(x5) x x2+43x95=0 x243x+95=0  a=1;b=43;c=95 D=b24ac=4324195=1469 D>0  x1,2=b±D2a=43±14692 x1,2=21.5±19.1637678967 x1=40.6637678967 x2=2.33623210326   Factored form of the equation:  (x40.6637678967)(x2.33623210326)=0  t1>0 t1=x1=40.6638=40.66 h

Our quadratic equation calculator calculates it.

t2>0 t2=t15=40.66385=35.66 h



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Showing 3 comments:
#
Math student
1/t1+1/(t1-10)=1/18
multiply each term by18(t1)(t1-10)
that results in
18(t1-10)+18t1=t1(t1)(t1)-10t1
using the quadratic formula results in t1=-49.6 and 3.63
ubless i made a mistake, your calculations need reexamination!!!        Correct me, please.

1 year ago  2 Likes
#
Dr Math
right side of equation is wrong - should be t1*(t1-10) = t12 - 10*t1 now t13-10t1

#
Math student
the problems seems to have changed - - - t2 is now equal t1-6

therefore 1/t1+1/(t1-6)=1/18
multiplying each term by18(t1)(t1-6) ==== 18(t1-6)+18t1=t1(t1-6), simplifying further 18t1-108+18t1=t12-6t1
or 0=t12-6t1-18t1+108
graphing y=18(t1-6)+18t1-t1(t1-6) results in t1=39.25 hours and t2=39.25-6=33.25 hours (same as your NEW answer!!!!

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