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Question Number 25937 by Mr eaay last updated on 16/Dec/17

F o r a c e r t a i n a m o u n t o f w o r k, A d e t a k e s

6 h o u r s l e s s t h a n B o d e . i f t h e y w o r k t o g e t h e r

i t t a k e s t h e m 13 h o u r s 20 m i n u t e s . H o w

l o n g w i l l i t t a k e B o d e a l o n e t o c o m p l e t e

t h e w o r k ?

Answered by ajfour last updated on 16/Dec/17

800 (A + B) m i n u t e s = W

T_{B} - T_{A} = 360 m i n u t e s

a s W = T_{A} A = T_{B} B

\Rightarrow \frac{W}{B} - \frac{W}{A} = 360

s o \frac{W}{B} - \frac{W}{(\frac{W}{800} - B)} = 360

a s T_{B} = \frac{W}{B} \Rightarrow

T_{B} - \frac{1}{(\frac{1}{800} - \frac{1}{T_{B}})} = 360

\frac{1}{T_{B} - 360} = \frac{1}{800} - \frac{1}{T_{B}}

\Rightarrow 800 T_{B} = (T_{B} - 800) (T_{B} - 360)

o r T_{B}^{2} - 1960 T_{B} + 800 \times 360 = 0, \Rightarrow

{(T_{B} - 980)}^{2} = 980 \times 980 - 800 \times 360

T_{B} = 980 + 20 \sqrt{49 \times 49 - 720}

= 980 + 20 \sqrt{2401 - 720}

= 980 + 20 \sqrt{1681}

= 980 + 20 \times 41 = 1800 m i n u t e s

= 30 h o u r s (B o d e a l o n e t a k e s) .

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