Question

In a surface mine bench, overburden is removed by shovel–dumper combination. Data for the dumper is given. Minimum number of dumpers required to avoid shovel idle time (in integer) is __________.

Hint:

Number of dumpers needed = cycle time / loading time; always round up.

Answer 1

Correct Answer: 14

Loading time:
\[ T_L = 3\ \text{min}. \]
Unloading time:
\[ T_U = 1\ \text{min}. \]
Travel distance (one-way):
\[ D = 4.5\ \text{km}. \]
Loaded speed:
\[ v_L = 12\ \text{km/hr} = 0.2\ \text{km/min}. \]
Travel time loaded:
\[ T_{loaded} = \frac{4.5}{0.2} = 22.5\ \text{min}. \]
Empty speed:
\[ v_E = 18\ \text{km/hr} = 0.3\ \text{km/min}. \]
Travel time empty:
\[ T_{empty} = \frac{4.5}{0.3} = 15\ \text{min}. \]
Total cycle time per dumper:
\[ T_{cycle} = T_L + T_U + T_{loaded} + T_{empty} = 3 + 1 + 22.5 + 15 = 41.5\ \text{min}. \]
Shovel loading time per dumper = 3 min. Number of dumpers required:
\[ N = \frac{T_{cycle}}{T_L} = \frac{41.5}{3} = 13.83. \]
Rounded up (integer):
\[ \boxed{14} \]