To clarify the intent of the question stem, I've replaced
how long with
how many hours:
Carcass wrote:
The constant rate at which machines A works is 34 of the constant rate at which machine B works. Under normal 4 conditions, machine A would complete x lots in 2 days. However, when a technician attempts to use machines A and B simultaneously, there is not enough electrical power to run both machines at full power. As a result, running the machines simultaneously reduces the work rate of each machine by 20%.
How many hours will it take the machines to complete 3x lots, working simultaneously?
Give your answer to the nearest 0.01.
The constant rate at which machines A works is 34 of the constant rate at which machine B works.
Let B's rate = 4 lots per day, implying that A's rate = 3 lots per day.
Under normal conditions, machine A would complete x lots in 2 days.Since x = the number of lots produced by A working at a rate of 3 lots per day for 2 days, we get:
x = (rate)(time) = 3*2 = 6 lots
Normal time for A and B to produce 6 lots
=workcombined−rate−for−A−and−B=63+4=67 days
Running the machines simultaneously reduces the work rate of each machine by 20%.
How many hours will it take the machines to complete 3x lots, working simultaneously?To produce 3x lots -- in other words, 3 times the amount of work -- A and B would normally require 3 times the number of days above:
3∗67=187 days
Rate and time have a RECIPROCAL RELATIONSHIP.
When the combined rate for A and B is reduced by 20%, the resulting rate is 4/5 their normal rate.
As a result, A and B will require 5/4 of their normal time:
54∗187 days
To convert from days to hours, we multiply by 24 (since there are 24 hours in each day):
54∗187∗24=77.14 hours