Two objects are located 390 meters away from each other on a straight

Question

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

A. 5
B. 10
C. 12
D. 15
E. 20

nick1816 · Answer

Distance travelled by first object in first 5 minutes= 18*5=90 (Eliminate option A)

After first 5 mins, distance b/w 2 objects=390-90=300

So both objects have to move 300m combined to meet.

We can also eliminate D and E option , since average speed of object 1 is more than 30/min after first 5 mins)

We left with option B and C.

Distance travelled by first object in next 5 mins= 48*5=240
Distance travelled by second object in these 5 mins= 12*5=60

combined distance = 240+60=300(what we looking for)

B

adkar · Answer

ANSWER B

Distance covered by object A in m minutes is 3m*(m+1), because the covered distance in n minutes is 6*(1+2+3+...+n) meters
Distance covered by object B in m minutes is 12m
Since object B starts moving after 5 min, object A already covered 90 meters (3*5*6), consequently the remaining distance to be covered is 300 meters.

Assume d'n is equal to the distance covered by object A after n+5 minutes such as d'1=6*(1+5), d'2=6*(2+5)+6*(1+5) etc., then d'n=6*(n+5)+6*(n-1+5)+6*(n-2+5)+...+6*(1+5) which is also equal to 30n+3*(n+1)

Now we solve 30n+3*(n+1)+12n=300 (with 300=390-90)
We find the second order equation  n^2+15n-100=0  where   5   is solution.
Since we are looking for the number of minutes after object A started moving, the Answer is B.

MathRevolution · Answer

First object ..............................(390 m) ...........................................Second object

First object: 6 , 12, 18, 24, 30, 36, ....

Second object: 12 , 12, 12, 12, ....

In first five minutes: First object has covered total distance of : 6 + 12 + 18 + 24 + 30 = 90.

Remaining distance is 390 - 90 = 300 m.

In next five minute distance covered :

First object: 36 + 42 + 48 + 54 + 60 = 240

Second object: 12 + 12 + 12 + 12 + 12 = 60

Total : 240 + 60 = 300

So, total 10 minutes.

Answer B

GMATGuruNY · Answer

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

B

Kinshook · Answer

Given: 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. 
Asked: In how many minutes after the first object started the movement will the two objects meet?

Distance covered by first object in t th minute = 6 + (t-1)6 = 6t
Total distance covered by first object after time t = 6 + 12 + ..... + 6t = 6 t(t+1)/2 = 3t(t+1)
Total distance covered by second object after time t = 12(t-5)
Since the two objects are moving towards each other, the Toal distance covered by 2 objects after time t = 3t(t+1) + 12(t-5) 
When they meet after time t, the total distance covered is 390 meters
3t(t+1) + 12(t-5) = 390
3t^2 + 3t + 12t - 60 = 390
3t^2 + 15t - 450 = 0
t^2 + 5t - 150 = 0
t^2 + 15t - 10t - 150 =0
(t+15)(t-10) = 0
t = 10 minutes

IMO B

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Two objects are located 390 meters away from each other on a straight

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