a carload of fraternity brothers leave their house for a long weekend trip. three hours later a second carload of brothers leaves the same house and travels the same path. if the second care drives and average of 15 mph faster than the first, what is the average speed of eavh car if it takes the second car six hours to catch up to the first
V1 = X mi/h
d1 = X * 3 = 3x miles head start.
V2 = (X+15)mi/h
(X+15)*T = X*T + 3x
(X+15)*6 = 6x + 3x
6x + 90 = 9x
3x = 90
X = 30 mi/h
X+15 = 30+15 = 45 mi/h.
Well, it seems like these fraternity brothers have quite the adventure on their hands! Let's break it down:
Let's assume the average speed of the first car is "x" mph. Since the second car is traveling 15 mph faster than the first car, its average speed would be "x + 15" mph.
Now, let's consider the time it takes for the second car to catch up to the first car. We know that it takes the second car six hours to catch up. Since the first car has a three-hour head start, it would mean that the first car has already traveled for three hours and the second car has traveled for six hours.
Now, since both cars travel the same path, the distance covered by the second car in those six hours is the same as the distance covered by the first car in three hours.
Distance = Speed * Time
For the first car:
Distance = x mph * 3 hours
For the second car:
Distance = (x + 15) mph * 6 hours
Since both distances are equal, we can set up an equation:
x mph * 3 hours = (x + 15) mph * 6 hours
Now, let's solve for x, the average speed of the first car.
3x = 6(x + 15)
3x = 6x + 90
Subtracting 6x from both sides:
-3x = 90
Dividing both sides by -3:
x = -30
Uh-oh! It seems like we've come across a problem here. Negative speed doesn't really make sense in this context, so maybe clown logic isn't the best fit for this question. You may want to double-check your numbers and ensure that the information provided is accurate. Good luck with your math puzzling!
To find the average speed of each car, we can use the formula speed = distance/time.
Let's assume the average speed of the first car is x mph. Therefore, the average speed of the second car is (x + 15) mph since it is driving 15 mph faster.
The first car has been traveling for 3 hours when the second car starts. So, the distance traveled by the first car is 3x miles.
Now, let's find the distance traveled by the second car when it catches up with the first car. Since both cars traveled the same path, they traveled the same distance.
The time taken by the second car to catch up with the first car is 6 hours. Therefore, the distance traveled by the second car is (x + 15) * 6 miles.
Since both cars traveled the same distance, we can equate the distances:
3x = (x + 15) * 6
Let's solve this equation to find the value of x:
3x = 6x + 90
-3x = 90
x = -30
Since we can't have a negative speed, the value of x is not valid in this context.
Hence, there is no solution to this problem.
To determine the average speed of each car, we can set up a distance equation based on the information provided.
Let's assume the average speed of the first car is x mph. Since the second car is driving 15 mph faster than the first car, its average speed would be (x + 15) mph.
We know that the second car catches up to the first car after traveling for 6 hours. We also know that the first car has already been traveling for 3 hours before the second car starts.
Since distance = speed × time, we can use this formula to set up the equation:
(distance covered by first car) + (distance covered by second car) = total distance
The first car has been traveling for 3 hours at a speed of x mph, so the distance it has covered is 3x miles.
The second car has been traveling for 6 hours at a speed of (x + 15) mph, so the distance it has covered is 6(x + 15) miles.
Setting up the equation:
3x + 6(x + 15) = total distance
Simplifying the equation:
3x + 6x + 90 = total distance
9x + 90 = total distance
Since both cars travel the same path, the total distance covered by each car is the same. Let's represent the total distance as "d".
9x + 90 = d
Now, we know that the second car catches up to the first car. This means that they have covered the total distance in the same amount of time. So, we can set up another equation:
(time taken by first car) = (time taken by second car)
The first car has been traveling for 3 hours before the second car starts, so its total time is (t + 3) hours.
The second car takes 6 hours to catch up to the first car.
Setting up the equation:
(t + 3) = 6
Simplifying the equation:
t + 3 = 6
t = 6 - 3
t = 3 hours
Since we now know the time taken by the first car is 3 hours, we can substitute it back into the equation for distance:
9x + 90 = d
9x + 90 = x * (t + 3)
9x + 90 = x * (3 + 3)
9x + 90 = 6x
Simplifying the equation:
9x - 6x = -90
3x = -90
Dividing both sides by 3:
x = -30
Since speed cannot be negative, we discard the negative value and conclude that x = 30.
Therefore, the average speed of the first car is 30 mph, and the average speed of the second car is 30 + 15 = 45 mph.