Question

Nathan owns a trucking company. For every truck that goes out, Nathan must pay the driver $20 per hour of driving and also has an expense of $2.75 per mile driven for gas and maintenance. On one particular day, the driver drove an average of 30 miles per hour and Nathan's total expenses for the driver, gas and truck maintenance were $820. Write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. Define the variables that you use to write the system.

Answer 1

Answer:

$m/h = 30$

$20h+2.75m=\ 820$

miles driven $m= 240\:miles$

hours driven $h= 8\:hours$

Step-by-step explanation:

Let us call $h$ the number of hours driven, and $m$ the number of miles traveled by a truck. Since on a particular day, the driver drove 30 miles per hour, we have:

$m/h = 30$

And since the total expenses for the driver and the truck were $820, we have:  

$20h+2.75m=\ 820$  (this says $20 per hour driven, and $2.75 per mile traveled must equal $820)

Thus we the system of equations:

$m/h = 30$

$20h+2.75m=\ 820$

From the first equation we get $m=30h$, and we put this into the second equation to get:

$20h+2.75(30h)=820$

solving for $h$, we get:

$\boxed{h= 8\: hours}$

Putting this value of $h$ into  $m=30h$ we get

$\boxed{m= 240 \:miles}$

Answer 2

The system of equations are ,  $\frac{y}{x} =30$   and  $20x+2.75y=820$

Total 8 hours driver worked and 240 miles truck drove.

Where variable x represent number of hours driven and variable y represent number of miles driven for gas and maintenance.

Let us consider, variable x represent number of hours driven and variable y represent number of miles driven for gas and maintenance.

Since, Nathan pay the driver $20 per hour of driving.

So, for x hours, paid by Nathan to driver, = 20x

Nathan also pay $2.75 per mile driven for gas and maintenance.

For y number of miles, = 2.75y

Since, Nathan's total expenses =  $820.

Equation represent,

                   $20x+2.75y=820 .............(1)$

Since, the driver drove an average of 30 miles per hour

   So,                      $\frac{y}{x} =30........(2)$

Substituting $y=30x$ in equation (1)

           $20x+2.75(30x)=820\\\\20x+82.5x=820\\\\x=8 hours$

So,   $y=30x=30*8=240miles$

Thus, 8 hours driver worked and 240 miles truck drove.

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