Question

Kate drove 180 miles on her vaca. She drove an average of 1.5 times faster on the 2nd 90 miles of her trip than she did the first. Which expression epresents the time she spent driving if x is her speed on the first 1/2 of her trip? Help me walk though this please....

Answer 1

\[a. \frac{ 150 }{ x } b. \frac{ 300 }{ x } c. 150x d. \frac{ 225 }{ x }\]

Answer 2

@jim_thompson5910 ?

Answer 3

rate * time = distance

Which expression represents the time ?

you know
time= distance/rate (re-arrange the equation rate*time=distance)

Answer 4

if you break the trip into 2 halves, each half is 90 miles

they tell you x is her speed on the first 1/2 of her trip

using time= distance/rate
you get time= 90/x (for the first half)

to get the time for the 2nd half of the trip you need to know the distance
you do, it is 90
you need to know the rate (the speed). they tell you She drove an average of 1.5 times faster on the 2nd 90 miles

if the speed on the first half is x, the speed on the second half is 1.5*x

putting it together: time(2nd half) = 90/(1.5x)

Answer 5

the total time is the sum of both halves:
\[ \frac{90}{x} + \frac{90}{1.5x} \]
this should be simplified ...
can you do that ?

Answer 6

one way to simplify is divide top and bottom of the 2nd fraction by 1.5
the top becomes 90/1.5 and the bottom becomes 1.5x/1.5 = x

Answer 7

ook, so would it be 150/x