Question

Jesse recently drove to visit her parents who live 126 miles away. On her way there, her average speed was 16 mph faster than on her way home (she ran into some bad weather). If Jesse spent a total of 4 hours driving find the two rates (in miles per hour). Round your answer to two decimal places if needed.

Answer 1

ANSWER

Jesse's average speed to her parent's house is 72 mph and her average speed from her parent's house is 56 mph

EXPLANATION

Let Jesse's average speed on her way home be x mph.

This implies that her average speed on her way to her parent's house is (x + 16) mph.

The average speed is given by:

$s=\frac{distance}{time}$

This implies that time is:

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

Hence, the total time spent by Jesse is:

$\frac{126}{x}+\frac{126}{x+16}\text{ }hrs$

We are given that the total time Jesse spent driving is 4 hours. This implies that:

$\frac{126}{x}+\frac{126}{x+16}=4$

Solve for x in the equation above:

$\begin{gathered} \frac{126(x+16)+126(x)}{x(x+16)}=4 \\ \\ \frac{126x+2016+126x}{x^2+16x}=4 \\ \\ \frac{252x+2016}{x^2+16x}=4 \\ \\ \Rightarrow4(x^2+16x)=252x+2016 \\ \\ 4x^2+64x=252x+2016 \\ \\ 4x^2+64x-252x-2016=0 \\ \\ 4x^2-188x-2016=0 \\ \\ \Rightarrow x^2-47x-504=0 \end{gathered}$

Solve for x by factorizing:

$\begin{gathered} x^2-56x+9x-504=0 \\ \\ x(x-56)+9(x-56)=0 \\ \\ (x+9)(x-56)=0 \\ \\ x=-9\text{ and }x=56 \end{gathered}$

Since speed cannot be negative, it implies that Jesse's average speed on her way home from her parent's house is:

$56\text{ }mph$

And her average speed on her way to her parent's house is:

$\begin{gathered} 56+16 \\ \\ \Rightarrow72\text{ }mph \end{gathered}$

That is the answer.