Question

A motorcycle rider travels at an average speed greater than $50$ miles per hour. Write and solve an inequality to determine how long it will take the motorcycle rider to travel $375$ miles. Explain your reasoning.

Answer 1

Step 1 : Write the inequality

Given : Average speed $>50$ miles per hour

Distance $=375$ miles.

We know that, $\frac{\mathbf{Distance}}{\mathbf{Time}}\mathbf{=}\mathbf{Speed}$

Let, the time taken to travel $375$ miles be $\mathrm{x}\mathrm{hours}$

Now, according to the question

Required inequality is $\frac{375}{\mathrm{x}}>50$

Step 2 : Solve the inequality

We have,$\frac{375}{\mathrm{x}}>50$

$$\begin{gathered} \Rightarrow \mathrm{x}<\frac{375}{50} \\ \therefore \mathrm{x}<7.5\mathrm{hours} \end{gathered}$$

Hence, the time required is less than $7.5\mathrm{hours}$.