Question

Question #235d2

Answer 1

`4 1/6` hours

Explanation:

Let's start with the first part, if Samantha is going 130 mph for 3 hours, we can determine how many miles she has gone total after those three hours by multiplying the speed by the time, or:

`d=v*t` where `d` is distance, `v` is speed and `t` is time
`d=130*3`
`d=390` miles

So now let's determine how many miles she has left, we know she has to go 500 miles total, and has already traveled 390, so:

`d_"left"=d_"total"-d_"traveled"`
`d_"left"=500-390`
`d_"left"=110` miles

She then sees a sign signifying a ten mile stretch, at which she slows to 60 mph. We know she went 10 miles distance at 60 mph, so we can determine the time taken by using the first equation again:

`d=v*t`
`d/v=t`
`10/60=t`
`t=1/6` hours

Now we know she has a certain distance left and goes this last stretch at 100 mph, so we can use the same method as above, but first we need to determine the distance she has left, so:

`d_"left"=d_"total"-d_"traveled"`
`d_"left"=500-390-10`
`d_"left"=100`

`d/v=t`
`100/100 = t`
`t=1` hour

So now we add up the time totals to get our answer,

`1+1/6+3=t_"total"`
`t_"total"=25/6` hours, or `4 1/6` hours

Hope this helps!