help..mathematics..?

Question

two brothers washed the family car in 24 mins. when they each wash the car alone, the younger brother took 20 mins longer to do the job than the older brother. how long did the older brother take to wash the car?(give quadratic eq'n)

Answer 1

quad eq: a^2 - 28 a - 480 = 0.

soln: a= 40 min.

i.e. Elder brother takes 40 min to wash the car.

steps:

a = time taken by elder brother
b= time taken by younger brother

1/a = work done in one unit time by E.B. (Assuming total work=1)
1/b = work done in one unit time by Y.B. (Assuming total work=1)

so, one unit time,

both can do 1/a + 1/b work.

Ques says both can do it in 24 min.

so, 1/a + 1/b = 1/24.------[1]


then, b = a + 20. -----------[2]
(obvious from the second clue in ques)

substitute [2] in [1].

get the quad eq. a^2 - 28 a - 480 = 0.
solve.
a=40.

Answer 2

Or you can look at this as a rate problem:

t is the time taken for older brother to wash 1 car. Therefore in 1 min, the older brother can wash 1/t cars. Similarly, younger brother washes 1/(t+20) cars in 1 min. It's given they can both wash 1 car in 24 mins, so together they can wash 1/24 cars in 1 min. Thus you can
form the sum:

1/t + 1/(t+20) = 1/24

t^2 - 28t - 480 = 0
implies t = -12 or t = 40 (but time can't be negative, so 40 is the answer)