Machine A can make 200 widgets in 14 hours, Machine B can make 200 wid

So we can safely forget the 0’s in the 200 and 100. since Machine A,B and C all made the same widget.

Rate of A (Ra) =2/14
Rate of B (Rb) =2/7=4/14
Rate of C (Rc)= 2/2=14/14

Total Rate (Rt) = R(a)+R(b)+R(c)
Total Rate (Rt) =2/14+4/14+14/14
(Rt) =20/14=10/7
Total work =1
R•T=W —> (10/7)•T=1 —> T=7/10(hrs)
T=7/10•60mins =42 mins

Answer B

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200= a14 = b7 = c2
We have to find k
(a+b+c)k = 100, replace the values of a,b and c.

I liked your approach of eliminating 3 options straight up. It shows the confidence even during the exam

Solution

Given:

• Machine A can make 200 widgets in 14 hours
• Machine B can make 200 widgets in 7 hours
• Machine C can make 200 widgets in 2 hours

To find:

• Time taken by them to complete 100 widgets when working together

Approach and Working Out:

• A + B + C can together make 200 widgets in \(1/(\frac{1}{14} + \frac{1}{7} + \frac{1}{2}) = \frac{14}{10} = \frac{7}{5}\) hours
• Therefore, they take \(\frac{1}{2} * \frac{7}{5} = \frac{7}{10}\) hours = 42 minutes to make 100 widgets

Hence, the correct answer is Option B.

Answer: B

for every 200 widgets combined rate ; 1/14+1/7+1/2 = 10/14 and total time ; 14/10 ; for half widgets ie 100 ; 14/10 * 1/2 = 7/10 hrs
in mins ; 7 * 60/10 ; 42 mins
IMO b

A-100 pins-7 hrs
B-100 pins-3.5hrs
C-100 pins- 1 hr

1/A+1/B+1/C=50/35

hence time is 35/50*60=42 mins

Machine A can make 200 widgets in 14 hours, Machine B can make 200 widgets in 7 hours, and Machine C can make 200 widgets in 2 hours. How long does it take them to complete 100 widgets when working together?

A. 32 minutes
B. 42 minutes
C. 84 minutes
D. 90 minutes
E. 96 minutes

Solution

Work(W) = Rate(R) * Time (T)

Work ( W) is given to be 200 for A, B, and C... lets keep it the way..

Rate for A = A's work / A's Time (from the formula)
= 200/14

Similarly B's Rate = 200/7

and

C's rate = 200/2 respectively.

Their collective rate (lets say K) will be A's rate + B's rate + C's rate. (as rates can be added)

Therefore,
K = 200/14 + 200/7 + 200/2 = 2000/14

they produce 2000 widgets in 14 hours

Now we're given a new work of 100 midgets..
which we can simply put in the formula
W = R * T
Rate we know for collective is 2000/14
and W = 100
therefore,
Time = 100/2000/14 = 100*14/2000 = 14/20

This will be in hours, now multiply it by 60 to get the value in minutes= 14*60/20 = 14*3 = 42

to get to answer option 42 mins (B)

The rate for Machine A is 200/14, for Machine B 200/7, and for Machine C 200/2. Thus, we can create the following combined rate:

200/14 + 200/7 + 200/2

200/14 + 400/14 + 1400/14 = 2000/14

So the time to completed 100 widgets is:

100/(2000/14) = 100 x 14/2000 = 14/20 = 42/60 hours = 42 minutes

Answer: B

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