fambrini wrote:A conveyer belt moves grain at the rate of 2 tons in 5 minutes and a second conveyer belt moves grain at the rate of 3 tons in 7 minutes. How many minutes will it take to move 20 tons of grain using both conveyer belts?
A) 12
B) 16 4/7
C) 18 3/6
D) 21
E) 24 4/29
We can classify this problem as a "combined worker" problem. To solve this type of problem we should use the formula:
Work (done by machine 1) + Work (done by machine 2) = Total Work Completed
It takes one conveyer belt 5 minutes to move 2 tons of grain, so the rate of conveyer belt 1 is 2/5. It takes the second conveyer belt 7 minutes to move 3 tons of grain, so the rate of conveyer belt 2 one is 3/7.
Since we know they are both working together to complete the job, we can label this unknown time as "t" for each conveyer belt during the time that both machines are working together. Since rate x time = work, we can multiply to get the work completed for each machine.
Work completed by conveyer belt 1 = (2/5)t
Work completed by conveyer belt 2 = (3/7)t
Finally, we can plug our two work values into the combined work formula to determine t. Since 20 tons of grain are moved, the total work completed is 20.
Work (done by conveyer belt 1) + Work (done by conveyer belt 2) = Total Work Completed
(2/5)t + (3/7)t = 20
Multiplying the entire equation by 35 gives us:
14t + 15t = 700
29t = 700
t = 700/29 = 24 4/29
Answer is
E
