Two Grape Crushers take 4 days to crush certain amount of grapes.If one of them crushed half the grapes and the other crushed other half , then they complete the job in 9 days. How many days will it take slower crusher to do the job alone?
my solution : the time taken when they both do 1/2 the work individually is 9 days given which means the slower guy took 9 days because consider A took 1 day he sits and waits for B to complete which he does on the 9th day right? so B will take double the time to complete double the work so 18 days is the answer according to me. But it doesnt make use of the first part of the Q. hence i am doubtful.
what do you guys think ? what is the correct method to solve this?
The jobs are done parallelly but not serially, one guy need not wait for the other to finish.
Wlog take the total weight of grapes to be 2 kg, their crushing speeds v1 and v2.
$$\dfrac{1}{v1}+\dfrac{1}{v2}=9$$
$$\dfrac{2}{v1+v2}= 4 $$
has solutions for speeds
$$\dfrac{1}{6},\dfrac{1}{3}; $$
For the slower crusher take the reciprocal, so the slow guy takes 6 days,
and for the faster one take reciprocal, so faster guy takes 3 days.