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?

Answer 1

45 mph

Let's call her speed in the city #x# mph Speed is miles per hour -speed=#(distance)/(time)# Rearranged Time = #(distance)/(speed)#

So in the city the time is #90/x# After the time is #130/(x+20# The total time is 4 hours So #90/x +130/(x+20)=4# The common denominator is #x(x+20)# So # (90(x+20)+130x)/(x(x+20))=4# #(90x+1800+130x)/(x^2+20x)=4# #220x+1800=4(x^2+20x)# Divide through by 4 #55x+450=x^2+20x# #x^2-35x-450=0# Factorise #(x-45)(x+10)=0# So #x=45# Check it out 90 miles at 45mph plus 130 miles at 65 mph is 4 hours

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Answer 2

Benjamin Altschul

To find Shari's speed in the city, you need to use the formula for average speed, which is total distance divided by total time.

Let's denote the speed in the city as $s$ mph.

Given:

Shari drove 90 miles in the city.
After that, she increased her speed by 20 mph on the highway and drove for 130 miles.
She drove for a total of 4 hours.

From the information given, we can set up the following equations:

$\text{Time spent in the city} = \frac{\text{Distance in the city}}{\text{Speed in the city}}$
$\text{Time spent on the highway} = \frac{\text{Distance on the highway}}{\text{Speed on the highway}}$
Total time = Time spent in the city + Time spent on the highway

Given that the total time is 4 hours, we can express this equation as:

$\text{Time spent in the city} + \text{Time spent on the highway} = 4$ hours

Now, let's plug in the given values:

$\frac{90}{s} + \frac{130}{s+20} = 4$

To solve for $s$ , the speed in the city, we need to solve this equation. Once we find $s$ , we will know Shari's speed in the city.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.