Question

Riley took a 4-hour drive. She went 112.5 miles before she got caught in a storm. Then she drove 45 miles at 15 mph less than she had driven when the weather was good. What was her speed driving in the storm?

Answer 1

Given

Riley drove 112.5 miles in the good weather ans 45 miles in the storm.

Time taken = 4 hour

Find

speed driving in the storm.

Step-by-step explanation

Let speed of Riley in the storm = x mph.

Let speed of Riley in good weather = x + 15 mph.

Time taken =

`(Distance)/(Speed)`

Time taken to drive 112.5 miles in good weather =

`t_1=(112.5)/(x+15).........................................({1})`

Time Taken to drive 45 miles in storm =

`t_2=(45)/(x).............................................({2})`

Now, the total time t, =

`\begin{gathered} 4=(112.5)/(x+15)+(45)/(x) \\ 4=(112.5x+45(x+15))/(x(x+15)) \\ 4\lbrack x(x+15)\rbrack=112.5x+45x+675 \\ 4x^2+60x=112.5x+45x+675 \\ 4x^2-97.5x-675=0 \end{gathered}`

by solving this quadratic equation , we get

`x=30`

Final Answer

The speed of Riley driving in the storm = 30 mph