Andrea made a car trip of 440 Kilometers. She averaged 54 Kilometers per hour for the frst part of the trip and 80 kilometers per hour for the secound part. If the total trip took 6 hours, how long was she traveling at 80 kilometers per hour?

See response in:

http://www.jiskha.com/display.cgi?id=1330042402

54.x+80.(6-x)=440

(54-80).x+480=440
26x=40
x=40/26=1,538
6-x=4.46 hours

To find the time Andrea spent traveling at 80 kilometers per hour, we can use the formula:

Time = Distance / Speed

Let's assume that Andrea spent x hours traveling at 80 kilometers per hour. We know that the total trip took 6 hours, so she must have spent (6 - x) hours traveling at 54 kilometers per hour.

For the first part of the trip, where Andrea traveled at 54 kilometers per hour, the time can be calculated as:

Time = Distance / Speed
(6 - x) = 440 / 54

Now, let's solve this equation for (6 - x):

(6 - x) = 440 / 54
6 - x = 8.15
-x = 8.15 - 6
-x = 2.15

Simplifying further, we have:

x = -2.15

Since time cannot be negative, this is not a valid solution. Thus, the question is most likely incorrect or there is missing information.

To determine how long Andrea was traveling at 80 kilometers per hour, we can use the equation:

Total Time = Time for First Part + Time for Second Part

We are given that the total trip took 6 hours. Let's assume Andrea traveled at 54 kilometers per hour for the first part and 80 kilometers per hour for the second part.

Let's represent the time for the first part as t1 and the time for the second part as t2.

We can formulate the equation as follows:

6 hours = t1 + t2

Next, we need to determine the distances traveled in each part of the trip by using the formula:

Distance = Rate × Time

For the first part, the distance traveled at 54 kilometers per hour is:

Distance for First Part = 54 kilometers per hour × t1

For the second part, the distance traveled at 80 kilometers per hour is:

Distance for Second Part = 80 kilometers per hour × t2

Since the total distance traveled is given as 440 kilometers, we can write the equation:

440 kilometers = Distance for First Part + Distance for Second Part

Substituting the previous equations into this equation, we get:

440 kilometers = 54 kilometers per hour × t1 + 80 kilometers per hour × t2

Now we have two equations:
6 hours = t1 + t2
440 kilometers = 54 kilometers per hour × t1 + 80 kilometers per hour × t2

To solve this system of equations, we can use either substitution or elimination method. Let's use the elimination method.

To eliminate the variables t1 or t2, we can multiply the first equation by 54 and the second equation by 6:

54 × (6 hours) = 54t1 + 54t2
6 × (440 kilometers) = 54t1 + 80t2

We now have two equations:
324 hours = 54t1 + 54t2
2640 kilometers = 54t1 + 80t2

Subtracting the second equation from the first equation, we can eliminate t1:

(324 hours) - (2640 kilometers) = (54t1 + 54t2) - (54t1 + 80t2)

-2316 = -26t2

Simplifying further, we have:

t2 = (-2316) / (-26) = 89.08 hours

Therefore, Andrea traveled at 80 kilometers per hour for approximately 89.08 hours.