Solve.
-One conveyor belt can move 1000 boxes in 7 minutes. Another can move 1000 boxes in 6 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) $42 \mathrm {~min}$
B) $\frac { 1 } { 42 } \mathrm {~min}$
C) $1 \frac { 5 } { 9 } \mathrm {~min}$
D) $\frac { 9 } { 14 } \mathrm {~min}$

Question

Quizplus · Accepted Answer

The first conveyor belt moves 1000 boxes in 7 minutes, so its rate is $1/7$ of the job per minute. The second moves 1000 boxes in 6 minutes, so its rate is $1/6$ of the job per minute. Together, they can do $(1/7 + 1/6)$ of the job per minute. When the third belt is added, all three complete the job in 3 minutes, meaning together they do $1/3$ of the job per minute. Let the rate of the third conveyor belt be $1/x$, where $x$ is the time in minutes it would take the third belt to move 1000 boxes alone. The equation is $1/7 + 1/6 + 1/x = 1/3$. Solving for $x$ gives $x = 42$ minutes.

Solve -One Conveyor Belt Can Move 1000 Boxes in 7 42 min42 \mathrm {~min}42 min

Solve
-One Conveyor Belt Can Move 1000 Boxes in 7 $42 \mathrm {~min}$