dsmaier wrote:
Can someone explain why the combined work formula doesn't work here? I understand your methodology, but keep getting 18 using that formula. Thanks!
Question: Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes. If robot A’s rate of polishing is 3/5 that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones?
You wish to use combined work formula: Let us do it:
Time taken by A and B to polish 88 pounds of gems = 6 minutes
Let time by B to polish 88 pounds of gems = x min
So time by A to polish 88 pounds of gems = 5x/3 min
=> time taken by A and B to polish 88 pounds of gems = (x)(5x/3)/(x + 5x/3) = 5x/8 minutes = 6 => x = 48/5 minutes
=> time by A to polish 88 pounds of gems = 5x/3 = 5/3 * 48/5 = 16 minutes
=> time by A to polish 1 pound of gems = 16/88 minutes
=> time by A to polish 165 pound of gems = 16/88 * 165 = 30 minutes
Obviously, it doesn't make sense to do it like this, since it is lengthy
So, let us improvise:
Question: Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes. If robot A’s rate of polishing is 3/5 that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones?
Rate of A = 3/5 of rate of B
thus: If B polishes 5x gems per minute => A will polish 3x gems per minute => Together they polish 8x gems per minute
thus, in 6 minutes they will polish 8x * 6 = 48x gems
thus, this 48x is actually 88
thus: 88 gems is 48x
=> 165 gems is 48x/88 * 165 = 90x gems
A was polishing 3x gems per minute
So, time = 90x/3x = 30 minutes
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