Question

Nancy took a 3 hour drive. She went 65 miles before she got caught in a storm. Then she drove 92 miles at 12 mph less than she had driven when the weather was good. What was her speed, in miles per hour, driving in the storm

Answer 1

Step-by-step explanation:

Let us start by listing out the given data:

To solve the question, we will make use of the basic formula:

`\begin{gathered} Distance=time* speed \\ time=(distance)/(speed) \end{gathered}`

Let the initial speed before she got caught in the storm will be V

For the first part, before she got caught in a storm. The time it will take Nancy before she got caught in the storm will be

`t_1=time=(distance)/(speed)=(65)/(V)`

Then for the second part, because her speed has reduced by 12,

the time when she drives in the storm be t2 can be obtained as

`t_2=(92)/(V-12)`

Finally, we can sum the times t1 and t2 and equate them to 3

`T=t_1+t_2=(65)/(v)+(92)/(v-12)=3`

We can solve for v as follow: Multiplying by the lcm

`65(v-12)+92(v)=3(v)(v-12)`

Simplifying further

`\begin{gathered} 65v-780+92v=3v^2-36v \\ 3v^2+101v+92v-780=0 \end{gathered}`

Solving for v

`\begin{gathered} v=60 \\ v=(13)/(3) \end{gathered}`

But since she drove 12 mph less than the initial speed. so it is not logical to pick 13/3 mph

Thus, the value of V is v = 60 mph

So the speed, when she drives in the storm is

`v-12=60-12\text{ =48mph}`

Therefore, the answer is 48 mph