Question

Mrs. Tucker can detail a car in 90 minutes, Mr. Smith can do it in 120 minutes. When they work with their son Tyler, they can detail a car in 30 minutes. How long would it take Tyler to detail a car by himself?

A. 60 minutes
B. 45 minutes
C. 40 minutes
D. 50 minutes

Answer 1

Tyler would take 45 minutes to detail a car by himself. (Option B)

The correct option is B,

Step-by-step explanation:

Let the rates of work for Mrs. Tucker, Mr. Smith, and Tyler be represented by T_T, T_S, and T_{Ty} respectively. The rates are given by the reciprocal of the time it takes for each person to detail a car.

T_T = 1 / 90, quad T_S = 1 / 120, quad T_{Ty} = 1 / T_y

When they work together, their combined rate is the sum of their individual rates:

T_T + T_S + T_{Ty} = 1 / 30

Now, substitute the given rates:

1 / 90 + 1 / 120 + 1 / T_y = 1 / 30

Combine the fractions:

2 / 180 + 1 / T_y = 1 / 30

Simplify:

1 / 90 + 1 / T_y = 1 / 30

Now, solve for T_y:

1 / T_y = 1 / 30 - \1 / 90

1 / T_y = 2/ 90

1 / T_y = 1 / 45

T_y = 45

Therefore, it would take Tyler 45 minutes to detail a car by himself.

So, the correct answer is:

B. 45 minutes

The correct option is B.