Question

A car traveling at a constant speed travels $1000\text{ft}$. in $12$ $seconds$. How long in hours will it take to travel $175$ $miles$?

Answer 1

Find the time taken to reach the distance travel $175$ $miles$.

We know that,

$$\begin{gathered} 1\text{ft}=0.000189\text{miles} \\ \Rightarrow 1000\text{ft}=0.189\text{miles} \end{gathered}$$

And

$$\begin{gathered} \Rightarrow 1\text{second}=0.000278\text{hour} \\ \Rightarrow 12\text{seconds}=0.00333\text{hour} \end{gathered}$$

Step-1: Find the speed travelled by the car:

We know that,

$\text{speed}=\frac{\text{distance travelled}}{\text{time}}$

Substitute $0.189\text{miles}$ for distance travelled and $0.00333\text{hour}$ for time in the above equation,

$$\begin{gathered} \text{speed}=\frac{0.189\text{miles}}{0.00333\text{hour}} \\ \text{speed}=56.7567\frac{\text{miles}}{\text{hour}} \end{gathered}$$

Thus, the speed of the car travelled is $56.7567miles/hour$

Step-2: Find time taken to reach the distance travel $175$ miles:

$$\begin{gathered} \Rightarrow \text{speed}=\frac{\text{distance travelled}}{\text{time}} \\ \Rightarrow \mathrm{time}=\frac{\text{distance travelled}}{\text{speed}} \end{gathered}$$

Substitute $175\text{miles}$ for distance travelled and $56.7567miles/hour$ for speed in the above equation,

$$\begin{gathered} \mathrm{time}=\frac{175\text{miles}}{56.7567{\displaystyle miles/hour}} \\ \mathrm{time}=3.0833\text{hours} \\ \mathrm{time}=3\text{hours} \end{gathered}$$

Hence, time taken to reach the distance travel $175$ miles is $3$ hours.