Question

Brian can build a model car twice as fast as Stewie. If they work together, they can build the model car in 3 hours. How much time would it take Stewie to build the car on his own?

A. 4.5 hours
B. 6 hours
C. 9 hours
D. 12 hours.

Answer 1

4.5 hours

Step-by-step explanation:

let the time Stewie use be X

let the time Brian use be ½X

if they work together

X+½X=3

X+X/2=3

find the LCM

2X+X /2 = 3

cross multiply

2X + X = 3*2

3X = 6

divide both side by the coefficient of X

X = 2

so if they work together

Stewie would work for 2 hours

Brian would work for 1 hour

and if Stewie was to build the car on his own

Answer 2

Stewie's work rate is approximately 1/9 cars per hour, which means it will take him 9 hours to build the model car alone, corresponding to option C.

Step-by-step explanation:

To determine how long it would take Stewie to build the model car on his own, we need to establish the rate at which Brian and Stewie work both together and individually. Let's denote Brian's work rate as B cars per hour and Stewie's work rate as S cars per hour. Given that Brian can build the model car twice as fast as Stewie, we have B = 2S. Since they can complete one car together in 3 hours, their combined rate is 1/3 cars per hour.

The formula for combined work is 1 = (B + S) × Time. Substituting the known values, we get:
1 = (2S + S) × 3
1 = 3S × 3
S = 1/9

Therefore, Stewie's rate is 1/9 cars per hour. To find out how many hours it takes Stewie alone to build the car, we calculate the reciprocal of his rate, which is 9 hours. Thus, it would take Stewie 9 hours to build the model car on his own, which corresponds to option C.