Answer:
45 miles per hour
Step-by-step explanation:
Time taken is given by distance/speed
Let speed on paved road be x hence on dirt road x-25
Time on paved road is [tex]\frac {135}{x}[/tex]
Time on dirt road is [tex]\frac {40}{x-25}[/tex]
The sum of these two time is equal to five hours hence expressed as
[tex]\frac {40}{x-25}+\frac {135}{x}=5\\5(x^{2}-25x)=40x+135x-3375\\5x^{2}-125x=175x-3375\\5x^{2}-300x+3375=0\\x^{2}-60x+675=0\\(x-15)(x-45)=0\\x=15 or 45[/tex]
Since speed was at a point reduced by 25, x can't be 15 hence x is 45.
