Question

A family is on a road trip. The speed limit during the first 165 miles of the trip is 65 mph, and the speed limit during the last 235 miles is 75 mph. How many miles per hour over the speed limits must they drive in order to arrive at their destination in 5.5 hours?

Answer 1

We must calculate the anwer eith the next approach

$\frac{165}{65+x}+\frac{235}{75+x}=5.5$

So, we need to solve for x

$\begin{gathered} \frac{165(75+x)+235(65+x)}{(65+x)(75+x)}=5.5 \\ \frac{12375+165x+15275+235x}{x^2+140x+4875}=5.5 \\ 27650+400x=26812.5+770x+5.5x^2 \\ 5.5x^2+370x=837.5 \\ x=-2.19,x=-69.46 \end{gathered}$

So, to arrive at their destination in 5.5 hours they must drive 2.19 mph over the speed limits.