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

Solution

From the question, First

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

$\begin{gathered} Speed=\frac{distance}{time} \\ x=\frac{205}{t} \\ t=\frac{205}{x} \\ Therefore,\text{ the time spent is given by} \\ time=\frac{205}{x} \end{gathered}$

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

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

Therefore, we equate the time

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

The answer is

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