Question

Please help me answer this math question. Please go through the steps clearly

Answer 1

The equation for car 2 is represented below as

`y=55x`

Where,

`\begin{gathered} x=\text{time (hours)} \\ y=\text{distance(miles)} \end{gathered}`

To calculate the average speed of each car, we will have to calculate the slope of the line

For car 2, when x= 1 hr

`\begin{gathered} y=55x \\ y=55*1 \\ y=55\text{miles} \end{gathered}`

When x=4 hrs,

`\begin{gathered} y=55x \\ y=55*4 \\ y=220\text{miles} \end{gathered}`

The average speed of car 2 will be calculated using the formula below

`\begin{gathered} \text{Average spe}ed=\frac{change\text{ in distance}}{\text{change in time}} \\ \end{gathered}`

By substituting the values, we will have

`\begin{gathered} \text{Average spe}ed=\frac{change\text{ in distance}}{\text{change in time}} \\ \text{Average spe}ed=(220-55)/(4-1) \\ \text{Average spe}ed=\frac{165\text{miles}}{3\text{hrs}} \\ \text{Average spe}ed=55\text{ miles/hr} \end{gathered}`

Hence,

The average speed of car 2 is 55 miles/hr

For car 1, when the value of x=1 hr

`y=64\text{ miles}`

When the value of x = 4hrs

`y=256\text{ miles}`

To calculate the average speed of Car 1 we will use the formula below

`\begin{gathered} \text{Average spe}ed=\frac{change\text{ in distance}}{\text{change in time}} \\ \text{Average spe}ed(=256-64)/(4-1) \\ \text{Average spe}ed=(192)/(3) \\ \text{Average spe}ed=64\text{ miles/hr} \end{gathered}`

Hence,

The average speed of car 1 is 64 miles/hr

Therefore,

Car 1 is travelling at a greater speed