Question

need some help with this question : When driving to their family reunion, River's mom drove 10 miles at a rate of x mph and then 25 miles at a rate of x + 10 mph . The total driving time was 45 minutes. What were the two driving speeds at which River's mom drove?

Answer 1

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

Time = $\dfrac{\textrm Distance}{\textrm speed}$

So, 45 = $\dfrac{10}{x}$ +  $\dfrac{25}{x + 10}$

Or, 9 = $\dfrac{2}{x}$ +  $\dfrac{5}{x + 10}$

Or, 9 × x × ( x + 10 ) = 2 × ( x + 10 ) + 5 x

Or, 9 x² + 90 x = 2 x + 20 + 5 x

Or, 9 x² + 90 x = 7 x + 20

Or, 9 x² + 90 x - 7 x - 20 = 0

Or, 9 x² + 83 x - 20 = 0

Solving this quadratic equation

x = $\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}$

Or, x = $\frac{-83\pm \sqrt{83^{2}-4\times 9\times (-20)}}{2\times 9}$

Or, x = $\frac{-83\pm \sqrt{7609}}{18}$

∴  x = $\frac{-83+87.22}{18}$ , tex]\frac{-83-87.22}{18}[/tex]

I.e x = 0.234 , - 9.4567

We 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   Answer