Question

For the same amount of work , a takes 6 hours less than



b. If together they complete the work in 13 hours 20 minutes ; find how much time will b alone take to complete the work. (ans:- b alone will take 30 hrs. To complete the work).

Answer 1

Answer:

B alone will take 30 hours to complete the work

A will take 30-6= 24 hours to complete the work

Step-by-step explanation:

let the time taken by  B = x hours

let the time taken by A =( x-6)hours

let A's one day work=1/x

B's one day work = 1/x-6

1/x+1/x-6=3/40

2x-6/x^2-6x = 3/40                           (on taking L.C.M)

On solving we get

3x^2 -98x +240 = 0

3x^2 -90x-8x +240 =0

3x(x-30) -8(x-30) =0

(x-30) (3x-8) =0                            

x=30 hours                                      (zero product rule)

Answer 2

Answer:

30 or 8/3 hours

Step-by-step explanation:

If B alone takes x hours then A will take x-6 hours.

Time taken by both to do work:

13+(20/60)

40/3

Thus,

1/x-6 + 1/x = 3/40

x+x-6/(x-6)x = 3/40

3 (x^2-6x) = 40 (2x-6)

3x^2-18x = 80x-240

3x^2-18x-80x+240=0

3x^2-90x-8x+240 = 0

3x (x-30) -8 (x-30) = 0

(3x-8)(x-30) = 0

Thus, x = 30 hours or x = 8/3

Because, x should not be fractional,

Thus, x = 30 hours

Therefore, B will take 30 hours to complete work