Question

Katalin drove 180 miles on her vacation. She drove an average of 1.5 times faster on the second 90 miles of her trip than she did on the first 90 miles of her trip. Which expression represents the time she spent driving? Let x = her speed on the first half of the trip.

A. 150/x
B. 300/x
C. 150x
D. 225/x

Answer 1

@Hope_nicole @ali2000

Answer 2

???

Answer 3

since 90 of it she spent it going 1.5x times faster than before..that means what?

Answer 4

Multiply?

Answer 5

Right? @Hope_nicole

Answer 6

so for 90 miles she was doing x and then for 90 miles she was doing 1.5x, so what equation would show that

Answer 7

Idk @Hope_nicole

Answer 8

@Mertsj @Mendicant_Bias

Answer 9

???

Answer 10

Can somebody please help me? I've been stuck on this and another problem for a long time.

Answer 11

Just give me a minute, lol. Thinking through it. I'd rather make sure that i'm doing it right than explain it wrong.

Answer 12

Got it. Just let me right it out.

Answer 13

*write

Answer 14

Okay

Answer 15

So, let's deal with what information we have available. We know that:

\[d = 180\]
Where d represents the total traveled distance.

\[v _{1} = x\]
Where v1 is the speed for the first 90 miles.

\[v _{2} = 1.5x\]
Where v2 is that speed times one and a half, right?

Since speed = distance/time, or
\[v = \frac{ d }{ t }\]
We can divide the distance by the velocity to get the time, like so:\[\frac{ \frac{ d }{ 1 } }{ \frac{ d }{ t } } = \frac{ d }{ 1 }*\frac{ t }{ d } = t\]
Now getting to the actual numbers:

Answer 16

The first 90 miles of her trip has a speed of x. So we have a speed and a distance. Now, we can find the time it took her to travel the first half.
\[\frac{ 90 }{ x } = t _{1}\]Where t1 is obviously the time it took for her to travel in the first half of the trip. Now, we just do the same with the second half:\[\frac{ 90 }{ 1.5x } = \frac{ 60 }{ x } = t _{2}\]Where t2 is the time it took her to travel in the second half of the trip. From here, we just add.\[\frac{ 60 }{ x }+\frac{ 90 }{ x } = \frac{ 150}{ x }\]

Answer 17

Does this make sense?

Answer 18

Well....get back to me when you get the chance. Hope this helps. You're welcome.