A person X can clean up all the crime in 4 hrs working alone. Person Y can do the same job in 10 hrs.

Question

If Person Y starts crime fighting at 9 AM, and person X joins him at 12 noon, what time will they have the crime cleaned up?

Answer 1

Person Y does 1/10 of the job in 1 hour.  Person X does 1/4 of the job in 1 hour.

 

If Person Y starts at 9 AM, by 12 PM (3 hours), 3*(1/10) = 3/10 of the crime has been cleaned up.  Therefore, there's only 7/10 of the crime left to be found at 12 PM.

 

Now, we set up an equation for the time when both person X and Person Y are fighting the crime:

 

If we let X = the number of hours it takes to clean up the crime after 12 pm

(1/4)*X + (1/10)*X = (7/10)  (because there's only 7/10 left of the crime to be fought)

 

Multiply the entire equation  by 20 to get rid of the fractions:

 

5X + 2X = 14

7X = 14

X = 2

 

Therefore, Person X and Person Y found crime together for 2 hours.  That means that all of the crime was cleaned up at 2 PM.

 

 

Answer 2

Y cleans crime at the rate of 1/10 per hour

X cleans crime at the rate of 1/4 per hour

In the first 3 hours that Y works alone he cleans up 3/10 of all crime

in the next n hours they will jointly clean at the rate of 

(1/4+1/10)*n = 7/10

multiply the equation by 2o on both sides

(5+2)*n = 14

solve for n=2 hours so both will finish the job by 2 PM

 

This assumes that the two crime fighters do not get into each others way when they try to work togehter - not exactly real life!