### Home > PC > Chapter 8 > Lesson 8.2.3 > Problem8-110

8-110.

On a recent 250 mile trip, Felicia averaged 50 mph over the first 125 miles. What should be her average speed for the second half of her trip, if she wants to average 60 mph over the whole journey? Homework Help ✎

$\text{Average Rate}=\frac{\text{total distance}}{\text{total time}}$

$\text{Average Rate}=\frac{250}{t_{\text{first}(125)}+t_{\text{second}(125)}}$

$\text{Average Rate}=\frac{250}{\frac{125}{50}+\frac{125}{r_2}}$

$60=\frac{250}{\frac{125}{50}+\frac{125}{r_2}}$

Multiply both sides by the denominator:

$\left(\frac{125}{50}+\frac{125}{r_2}\right)(60)=250$

$\frac{(125)(60)}{50}+\frac{(125)(60)}{r_2}=250$

Multiply each term by 50r2.

$(125)(60)(r_2)+(125)(60)(50)=250(50\textit{r}_2)$

375000 = 5000r2

r2 = 75 mph