Ami, Bhami and Chani started working on a project. All three of them working together take two hours to complete

Mikrislac wrote: ↑

Wed Jul 29, 2020 9:24 am

Ami, Bhami and Chani started working on a project. All three of them working together take two hours to complete the project. Chani individually takes four times the amount of time taken by Ami and Bhami working together. Ami takes half the amount of time that is taken by Bhami and Chani working together. What is the fractional amount of work that Bhami can complete in one hour?

A. 1/4
B. 1/5
C. 1/6
D. 1/12
E. 1/15

Solution:

We can let the project = 60 (we choose the number 60 since it’s the least common denominator of all the denominators in the answer choice). We can let A, B, and C be the hourly rates of Ami, Bhami, and Chani, respectively. We can create the equations (recall that rate is inverse of time):

A + B + C = 60/2 → A + B + C = 30

C = ¼(A + B) → 4C = A + B

and

A = 2(B + C) → A = 2B + 2C

Substituting 4C for A + B in the first equation, we have:

4C + C = 30

5C = 30

C = 6

Substituting 2B + 2C for A in the first equation, we have:

2B + 2C + B + C = 30

3B + 3C = 30

B + C = 10

Since C = 6, we have:

B + 6 = 10

B = 4

Since the project is 60 and B’s hourly rate is 4, Bhami can complete the 4/60 = 1/15 of the project in one hour.

Answer: E