Solve.
-One conveyor belt can move 1000 boxes in 8 minutes. Another can move 1000 boxes in 10 minutes. If another conveyor belt is added and all three are used, the boxes are moved in 3 minutes. How long would it take the
Third conveyor belt alone to do the same job?
A) $9 \frac { 3 } { 13 }$ m minutes
B) $\frac { 67 } { 120 }$ m minutes
C) $1 \frac { 53 } { 67 }$ m minutes
D) $\frac { 13 } { 120 }$ m minutes

Question

Quizplus · Accepted Answer

The first conveyor belt moves 1000 boxes in 8 minutes, so its rate is $ \frac{1000}{8} = 125 $ boxes per minute. The second moves 1000 boxes in 10 minutes, so its rate is $ \frac{1000}{10} = 100 $ boxes per minute. Together, they move $ 125 + 100 = 225 $ boxes per minute. When all three are used, they move 1000 boxes in 3 minutes, which is a rate of $ \frac{1000}{3} $ boxes per minute. The third conveyor belt's rate is the total rate minus the first two belts' rates, which is $ \frac{1000}{3} - 225 = \frac{1000 - 675}{3} = \frac{325}{3} $ boxes per minute. To find how long it takes the third belt to move 1000 boxes alone, we divide the total number of boxes by its rate: $ \frac{1000}{\frac{325}{3}} = \frac{1000 \times 3}{325} = \frac{3000}{325} = \frac{120}{13} = 9 \frac{3}{13} $ minutes.

Solve -One Conveyor Belt Can Move 1000 Boxes in 8 93139 \frac { 3 } { 13 }9133​

Solve
-One Conveyor Belt Can Move 1000 Boxes in 8 $9 \frac { 3 } { 13 }$