Alejandro, working alone, can build a doghouse in 4 hours. Betty can

Question

Alejandro, working alone, can build a doghouse in 4 hours. Betty can build the same doghouse in 3 hours. If Betty and Carmelo, working together, can build the doghouse twice as fast as Alejandro, how long would it take Carmelo, working alone, to build the doghouse?

A. 5.5 hours
B. 6 hours
C. 7 hours
D. 8 hours
E. 9 hours

A. 5.5 hours
B. 6 hours
C. 7 hours
D. 8 hours
E. 9 hours

Kinshook · Answer

Let us assume that Carmelo can build the doghouse in x hrs

\frac{1}{3} + \frac{1}{x} = \frac{1}{2}

Gives x = 6

IMO B

CareerGeek · Answer

Assume the work = 12 units

Rate of A = 12/4 = 3 units per hour
Rate of B = 12/3 = 4 units per hour

Given,  R_B  +  R_C  = 2 R_A 
-->  R_C  = 2*3 - 4 = 2 units per hours

Time taken for C = 12/2 = 6 hours

IMO Option B

Pls Hit kudos if you like the solution

Archit3110 · Answer

given 
1/3+1/c= 1/4*2
solve for c= 6 hrs
IMO B

ScottTargetTestPrep · Answer

Since Betty and Carmelo, working together, can build the doghouse twice as fast as Alejandro, they can build 2 doghouse in 4 hours or 1 doghouse in 2 hours. If we let c = the time it takes Carmelo, working alone, to build the doghouse, we can create the equation:

1/3 + 1/c = 1/2

Multiplying by 6c, we have:

2c + 6 + 3c

6 = c

Answer: B

Alejandro, working alone, can build a doghouse in 4 hours. Betty can

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Alejandro, working alone, can build a doghouse in 4 hours. Betty can

Prep Toolkit

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