sherxon wrote:
Two objects are located 390 meters away from each other on a straight path. The first object covers 6 meters in the first minute, and the distance covered in every next minute is 6 meters greater than that in the previous minute. The second object moves at a speed of 12 meters per minute. The first object starts to move toward the second one, and after 5 minutes the second object starts moving toward the first one. In how many minutes after the first object started the movement will the two objects meet?
A. 5
B. 10
C. 12
D. 15
E. 20
For any EVENLY SPACED SET:
sum = (count)(median)
For the first five minutes, only the first object travels.
Minutes 1-5:
Since the initial 6 meter-per-minute rate for the first object increases by 6 meters each minute, we get the following set of evenly spaced distances:
6, 12, 18, 24, 30
sum = (count)(median) = 5*18 = 90
From this moment on, the two objects travel toward each other.
When objects travel toward each other, they WORK TOGETHER to cover the distance between them.
As a result, we ADD THEIR RATES.
Next minute:
Distance traveled by the first object = (previous distance) + (6 additional meters) = 30+6 = 36
Distance traveled by the second object = 12
Combined rate for the two objects = 36+12 = 48
Minutes 6-10:
Since the first object increases the rate by 6 meters each minute, we get the following set of evenly spaced distances:
48, 54, 60, 66, 72
sum = (count)(median) = 5*60 = 300
In minutes 1-10, the total distance traveled = 90+300 = 390
Thus, the total time for the 390-meter distance to be traveled = 10 minutes