Shari drove for 90 miles in the city. When she got on the highway, she increased her speed by 20 mph and drove for 130 miles. If Shari drove a total of 4 hours, how fast did she drive in the city?
(90 / c) + [130 / (c + 20)] = 4
90 c + 180 + 130 c = 4 c^2 + 80 c
c^2 - 35 c - 45 = 0
use quadratic formula to find c
typo error in 90 c + 180 + 130 c = 4 c^2 + 80 c
should be : 90 c + 1800 + 130 c = 4 c^2 + 80 c
---> c^2 - 35c - 450 = 0
(c - 45)(c + 10) = 0
c = 45 or a negative
city speed was 45 mph
thanks for the catch, Reiny
too late to be working on this stuff
To find out how fast Shari drove in the city, we can use the formula for speed, which is distance divided by time.
Let's break down the information given:
Shari drove for 90 miles in the city.
Shari increased her speed by 20 mph on the highway.
Shari drove for 130 miles on the highway.
Shari drove a total of 4 hours.
First, let's find the time Shari spent driving in the city. We can do this by subtracting the time spent on the highway from the total time.
Total time - Time spent on the highway = Time spent in the city
We know that the total time is 4 hours and the time spent on the highway is the distance divided by the increased speed:
Time spent on the highway = Distance on the highway / Increased speed
Time spent on the highway = 130 miles / (Increased speed)
Now we can substitute this into the equation:
4 hours - (130 miles / Increased speed) = Time spent in the city
Next, let's find the speed Shari drove in the city. We can do this by dividing the distance traveled in the city by the time spent in the city:
Speed in the city = Distance in the city / Time spent in the city
Speed in the city = 90 miles / (4 hours - (130 miles / Increased speed))
Simplifying this equation, we can multiply both sides by the denominator:
Speed in the city * (4 hours - (130 miles / Increased speed)) = 90 miles
Expanding the equation:
4 hours * Speed in the city - (130 miles / Increased speed) * Speed in the city = 90 miles
Combining like terms, we get:
(4 hours - (130 miles / Increased speed)) * Speed in the city = 90 miles
Finally, to solve for Speed in the city, divide both sides by the expression in front of it:
Speed in the city = 90 miles / (4 hours - (130 miles / Increased speed))
Now we have the equation to find the speed Shari drove in the city. To solve it, we need to plug in the given information and solve for Increased speed.
Please note that without knowing the value of Increased speed, we cannot determine the exact speed Shari drove in the city.