lean can paint her new apartment 3 hours longer than his friend,carlos.if both can do painting in 2 hours,how long will it take each one to finish the job alone?
labour*time=job time=job/labour
time=3 and 3x=1 x=1/3
If both can do painting in 2 hours,So
(x+y)2=1 x=1/3 hence (1/3+y)*2=1
And y is 1/6.We can say that it take 6hours to finish the job alone.
let Carlos' time be x hrs
so rate for Carlos = 1/x
Lean's time is x+3
Lean's rate = 1/(x+3)
combined rate = 1/x + 1/(x+3)
= (x+3 + x)/(x(x+3)) = (2x+3)/(x(x+3))
1/[ (2x+3)/(x(x+3))] = 2
x(x+3)/(2x+3) = 2
x^2 + 3x = 4x + 6
x^2 - x - 6 = 0
(x-3)(x+2) = 0
x = 3 or x=-2, the latter is not possible
Carlos would take 3 hrs, and Lean would take 6 hrs alone
check:
combined rate = 1/3 + 1/6 = 1/2
combined time = 1/(1/2) = 2
Keiko bicycles 4km/h faster than Carlos. In the same time it takes Carlos to Bicycle 45km, Keiko can bicycle 57km. How fast does each bicyclist travel?
To find out how long it will take Lea and Carlos to finish the job individually, we can start by determining their individual painting rates based on the given information.
Let's assume that Carlos can complete the entire painting job in x hours. Since Carlos can complete the job in 2 hours together with Lea, we can say that Carlos's painting rate is 1/x of the job per hour.
According to the problem, Lea takes 3 hours longer than Carlos to finish the job. Therefore, Lea's painting rate would be 1/(x+3) of the job per hour.
We now have the following equation based on their combined rate of finishing the job in 2 hours:
1/x + 1/(x+3) = 1/2
To solve this equation, we can use the concept of finding a common denominator and simplifying:
2(x+3) + 2x = x(x+3)
2x + 6 + 2x = x^2 + 3x
4x + 6 = x^2 + 3x
0 = x^2 - x - 6
At this point, we have a quadratic equation that can be factored or solved using the quadratic formula. Factoring this equation gives us:
0 = (x - 3)(x + 2)
Setting each factor equal to zero gives us the possible values for x:
x - 3 = 0 or x + 2 = 0
Solving these equations, we find:
x = 3 or x = -2
Since we are looking for a positive value, we can discard the solution x = -2.
Therefore, Carlos can finish the job alone in 3 hours, while Lea can finish the job alone in 3 + 3 = 6 hours.