jain2016 wrote:Since rate and time are RECIPROCALS, we get:
(A's time)/(B's time) = 5/4.
Hi Mitch ,
Can you please explain why Reciprocal ?
I Don't understand the above part.
Many thanks in advance.
SJ
Rate the time have a RECIPROCAL relationship.
If A works 3 times as fast as B, then A's time will be 1/3 B's time.
To illustrate:
Let A's rate = 3 widgets per hour and B's rate = 1 widget per hour, with the result that A works
3 times as fast as B.
Time for A to produce 3 widgets = w/r = 3/3 = 1 hour.
Time for B to produce 3 widgets = w/r = 3/1 = 3 hours.
Result:
A's time (1 hour) is equal to
1/3 B's time (3 hours).
If A's time is 1/2 B's time, then A works twice as fast as B.
To illustrate:
Let A's time to produce 2 widgets = 1 hour and B's time to produce 2 widgets = 2 hours, with the result that A's time is
1/2 B's time.
A's rate = w/t = 2/1 = 2 widgets per hour.
B's rate = w/t = 2/2 = 1 widget per hour.
Result:
A's rate (2 widgets per hour) is
twice B's rate (1 widget per hour).
In the problem posted above, (A's rate)/(B's rate) =
4/5.
Thus, (A's time)/(B's time) =
5/4.
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