Answer:
The speed of River's mom drove for 10 miles distance is 0.234 mph.
The speed of River's mom drove for 25 miles is 10.234 mph.
Step-by-step explanation:
Given as :
The first distance cover by River's mom = 10 miles
The rate of speed = x mph
The second distance cover by river's mom = 25 miles
The rate of speed = x + 10 mph
The total driving time = 45 min
Now, According to question
[tex]Time = \frac{Distance}{Speed}[/tex]
So, [tex]45 = \frac{10}{x}+\frac{25}{x+10}[/tex]
Now dividing by 5 on both side we get;
[tex]9=\frac{2}{x}+\frac{5}{x+10}\\\\9= \frac{2(x+10)+5x}{x(x+10)}\\\\9= \frac{2x+20+5x}{x^2+10x}\\\\9(x^2+10x)= 7x+20\\9x^2+90x-7x-20=0\\9x^2+83x-20=0[/tex]
Solving this quadratic equation we get;
[tex]x=\frac{-b\±\sqrt{4ac}}{2a}[/tex]
[tex]x=\frac{-83\±\sqrt{4\times9 \times 20}}{2\times 9}\\\\x= \frac{-83\±\sqrt{720}}{18}\\ \\x= \frac{-83+87.22}{18} \ \ \ or \ \ x = \frac{-83-87.22}{18}\\\\x= 0.234 \ \ \ or\ \ \ \ x= - 9.4567[/tex]
Since speed cannot be in negative hence we will consider x= 0.234
So, The speed for 10 miles distance = x = 0.234 mph
and The speed of 25 miles = x + 10 = 0.234 + 10 = 10.234 mph
Hence The speed of River's mom drove for 10 miles distance is 0.234 mph
and The speed of River's mom drove for 25 miles is 10.234 mph
