Question

Hey can anyone help me with this problem

Answer 1

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.

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

`Time = (Distance)/(Speed)`

So,
`45 =  (10)/(x)+(25)/(x+10)`

Now dividing by 5 on both side we get;

`9=(2)/(x)+(5)/(x+10)\\\\9= (2(x+10)+5x)/(x(x+10))\\\\9= (2x+20+5x)/(x^2+10x)\\\\9(x^2+10x)= 7x+20\\9x^2+90x-7x-20=0\\9x^2+83x-20=0`

Solving this quadratic equation we get;

`x=(-b\±√(4ac))/(2a)`

`x=(-83\±√(4*9 * 20))/(2* 9)\\\\x= (-83\±√(720))/(18)\\ \\x= (-83+87.22)/(18) \ \ \ or \ \ x = (-83-87.22)/(18)\\\\x= 0.234 \ \ \ or\ \ \ \ x= - 9.4567`

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