The 8th grade class is taking a field trip to a concert. Your bus averages 40 mph in the heavy traffic driving to the concert and 60 mph returning home. The total travel time is 2.5 hours. How far away is the concert? How long did it take to get to the concert?
5 mins.
its over 9000!!!
To find the distance to the concert, we first need to determine the time it took to get there. Let's assign a variable for this unknown:
Let's say the time taken to get to the concert is represented by t, in hours.
Now, we can use the formula:
Distance = Speed * Time
For the trip to the concert, the bus averaged 40 mph and the time taken was t hours. So the distance to the concert would be:
Distance to concert = 40 mph * t hours = 40t
Next, let's calculate the time taken for the return trip.
The bus averaged 60 mph and the total travel time was 2.5 hours.
So, the time taken for the return trip would be:
Return trip time = Total travel time - Time taken to get to the concert
Return trip time = 2.5 hours - t hours = 2.5 - t
Now, we know that the return trip time was 2.5 - t hours and the speed was 60 mph.
Using the formula again, we can find the distance for the return trip:
Distance of return trip = 60 mph * (2.5 - t) hours = 150 - 60t
Since the total distance covered is the sum of the distances for the trip to the concert and the return trip, we can set up the following equation:
Distance to concert + Distance of return trip = Total distance
40t + (150 - 60t) = Total distance
Now, we have the equation:
40t + 150 - 60t = Total distance
Combining like terms:
-20t + 150 = Total distance
To find the total distance, we need to know the total travel time, which is given as 2.5 hours.
We know that distance = speed * time, so the total distance can also be expressed as:
Total distance = (40 mph + 60 mph) * 2.5 hours = 100 miles
Now, we have the equation:
-20t + 150 = 100
To solve for t, we can subtract 150 from both sides of the equation:
-20t = -50
Finally, we divide both sides of the equation by -20 to solve for t:
t = -50 / -20
t = 2.5 hours
Therefore, it took 2.5 hours to get to the concert.
To find the distance to the concert, we substitute t back into our equation for distance:
Distance to concert = 40t
Distance to concert = 40 * 2.5 = 100 miles
Therefore, the concert is 100 miles away.