Question

a contractor knows that it would take 4 days longer for a small dump truck to order a haul of gravel to a construction site than a large one to haul the same order. By using 8 small and 6 large dump trucks working together, the order was delivered in 1 day. Find the number of days it would have taken one small truck, working alone, to deliver the gravel.

Answer 1

We have to write the conthitions that are given to us so:

1) 8 small (S) and 6 large (L) finish in one day so we can write it like:

`8S+6L=1`

2) a small (S) takes 4 days more than a large (L) one to do the same work so we can put it like:

`\begin{gathered} L=x \\ S=x+4 \end{gathered}`

we solve the secon one for x so:

`S-4=x`

then we can make the equation equal:

`L=S-4`

we can replace this expretion into the first equation to know how long it would take to do it just with small trucks so:

`8S+6(S-4)=1`

and we solve for S so:

`\begin{gathered} 8S+6S-24=1 \\ 14S=25 \end{gathered}`

this means that 14 small trucks would take 25 days to finish the work so now we can made a rule of 3 to find the tame that takes to just one truck so:

`\begin{gathered} 14\to25 \\ t=14\cdot25=350 \end{gathered}`

it would take 350 days to finis the work for one small truck