Question $4$:

a$.$ A wheel tractor$-$scraper whose weight on the driving wheels is $16,667kg$ has a gross weight of $40,000kg.$ If the road surface is wet earth with a rolling resistance factor of $80k\frac{g}{t},$ what is the maximum grade the scraper could ascend?

$(3$ marks$)$

b$.$ Crushed stone is delivered from a pit located $10km$ to fill an excavated site. The swell for the crushed stone is $10\%.$ A $11m^3$ truck capacity used to transport the crushed stone. The loader loads material at the pit at a rate of $50\frac{m^3}{h}r.$ The trucks travel at an average speed of $25k\frac{m}{h}r$ going and returning and take $9$ minutes for unloading at the site. Calculate the required number of trucks.

$(4$ marks$)$