During a hurricane evacuation from the east coast of Georgia, a family traveled west. For part of the trip, they averaged but as the congestion got bad, they had to slow to If the total time of travel was 7 hours, how many miles did they drive at the reduced speed?
5 hours
unless you have some speeds or distances that indicate otherwise...
To solve this problem, we need to use the formula:
Average speed = Total distance / Total time
Let's assume the distance they traveled at the average speed was x miles. Since the total time of travel was 7 hours, we can set up the following equation:
x / 60 + (x / 40) = 7
Let's solve this equation step by step:
1. Multiplying each term in the equation by 120 (the least common multiple of 60 and 40) to eliminate the denominators:
2(x) + 3(x) = 7 * 120
2x + 3x = 840
5x = 840
2. Dividing both sides of the equation by 5:
x = 840 / 5
x = 168
So, the distance they traveled at the average speed of 60 mph was 168 miles.
Now, we need to determine the distance they traveled at the reduced speed of 40 mph. Since they traveled for a total of 7 hours, and the part of the trip at the average speed of 60 mph took x / 60 hours, we can find the time spent at the reduced speed:
Total time - Time at average speed = Time at reduced speed
7 - (x / 60) = Time at reduced speed
Substituting the value of x we found earlier:
7 - (168 / 60) = Time at reduced speed
7 - (2.8) = Time at reduced speed
4.2 = Time at reduced speed
The time at the reduced speed is 4.2 hours.
To find the distance they traveled at the reduced speed, we multiply the time by the speed:
Distance = Speed * Time
Distance = 40 * 4.2
Distance = 168
Therefore, the family drove 168 miles at the reduced speed during the hurricane evacuation.