Christian went on a run. He jogged for five minutes, then increased his rate to a faster constant pace for seven minutes. He then took a rest for four minutes. During what time interval has Christian traveled 1.5 miles?
(1 point)
Christian traveled 1.5 miles from blank ≤t≤ blank
.
To solve this problem, we need to find the time interval during which Christian traveled 1.5 miles. Given that Christian jogged for 5 minutes and then increased his pace for 7 minutes, we can calculate the total distance covered during this time.
The formula to calculate distance is given by:
Distance = Speed * Time
Let's assume Christian's speed during the first 5 minutes was "s1" miles per minute, and the speed during the next 7 minutes was "s2" miles per minute. Given that Christian jogged for 5 minutes at speed s1, we can calculate the distance covered during this time as:
Distance1 = s1 * 5 minutes
Similarly, during the next 7 minutes at speed s2, the distance covered would be:
Distance2 = s2 * 7 minutes
Adding both distances, we can calculate the total distance covered in 12 minutes (5 + 7 minutes):
Total Distance = Distance1 + Distance2
Now, we can equate the total distance to 1.5 miles and solve for the speed. Assuming the speed remains constant throughout the jog:
Total Distance = 1.5 miles
Now, we have the equation:
1.5 miles = (s1 * 5 minutes) + (s2 * 7 minutes)
Given that Christian then took a rest for 4 minutes, the total time elapsed would be 5 + 7 + 4 = 16 minutes.
So, the time interval during which Christian traveled 1.5 miles is:
0 ≤ t ≤ 16 minutes.
Note: The specific values for s1 and s2 are not given in the question, so it's not possible to determine the exact time interval without additional information.