Question

Elaine drives her car 205 miles and has an average of a certain speed. If the average speed had been 4mph more, she could have traveled 225 miles in the same length of time. What was her average speed?

Answer 1

From the question, First

Let x be the avreage speed Elaine used to travel on his car 205 miles

`\begin{gathered} Speed=(distance)/(time) \\ x=(205)/(t) \\ t=(205)/(x) \\ Therefore,\text{ the time spent is given by} \\ time=(205)/(x) \end{gathered}`

Assuming the average speed has been 4mph more, so we have

`\begin{gathered} Speed=(distance)/(time) \\ x+4=(225)/(t) \\ t=(225)/(x+4) \\ Therefore,\text{ the same time as the first will be} \\ time=(225)/(x+4) \end{gathered}`

Therefore, we equate the time

`\begin{gathered} (205)/(x)=(225)/(x+4) \\ cross\text{ multiply} \\ \text{225}* x=205(x+4) \\ 225x=205x+820 \\ 225x-205x=820 \\ 20x=820 \\ x=(820)/(20) \\ x=41 \\ Therefore, \\ x=41mph \end{gathered}`

The answer is

`\begin{equation*} 41mph \end{equation*}`