GMAT Club Olympics 2024 (Day 9): Jerry starts running from the house

Question

Jerry starts running from the house to the barn, which is 150 meters away, at a constant speed of 2 meters per second. After 10 seconds, Tom starts running from the barn to the house at a constant speed of 3 meters per second. What will be Jerry's distance from their meeting point when Tom reaches the house?

A. 24 meters
B. 30 meters
C. 40 meters
D. 48 meters
E. 78 meters

A. 24 meters
B. 30 meters
C. 40 meters
D. 48 meters
E. 78 meters

Bunuel · Accepted Answer

GMAT Club Official Explanation:

In the initial 10 seconds, Jerry would cover 10 seconds * 2 meters per second = 20 meters. Thus, by the time Tom starts running, the distance between them would be 150 meters - 20 meters = 130 meters. Their combined speed is 2 meters per second + 3 meters per second = 5 meters per second, so they would cover that distance in 130 meters / 5 meters per second = 26 seconds. In these 26 seconds, Jerry would cover an additional 26 seconds * 2 meters per second = 52 meters. Therefore, Jerry's total distance covered to the meeting point from the house would be 52 meters + 20 meters = 72 meters.

Hence, Tom needs to cover those 72 meters to reach the house. Since the ratio of their speeds is 3 to 2, the distances they cover in the same time would be in the same ratio. Thus, in the time Tom would need to cover 72 meters, Jerry would cover 48 meters (since 72/d = 3/2, solving for d yields d = 48).

Answer: D.

RishS94 · Answer

In First 10 sec Jerry moves to 20 m. Tom is at 0 mtrs from his starting point.

So 130mtrs left between Tom & Jerry.

130mtrs is covered at speed 5m/s as while running towards each other speed will be added (2m/s+3m/s)

So in 130/5 = 26 secs Jerry & Tom will meet.

>>>20>>>>>>>>>>>>>J>>>>>>>>>>>130 mtrs>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>T

In next 26 secs,
|Intially covered 20 mtrs|>>>Jerry covers 52 mtrs>> |Meeting point|<<<<<<<<<< Tom covers 78 mtrs<<<<<<<|

Tom takes 50 sec to reach home (150mtrs/ 3m/s).

So after 50 secs Jerry will be 100 mtrs away from his first lead point. (This excludes first 20 mtrs)

So Jerry will be 100-52 = 48 mtrs away from meeting point.

Milkyway_28 · Answer

I liked this question a lot. So there are quite a lot of small pieces of information to take into acount.

We know that Jerry and Tom are running toward each other from two points, the House and the Barn, situated 150 meters apart, at 2 meters per second and 3 meters per second respectively. The first piece of vital information is that Tom starts running 10 seconds after Jerry. So the way I calculated this was that I first calculated what Jerry ran in 10 seconds, which is 2*10 = 20 meters. I subtracted 20 from 150 and then treated the question as if they started running towards each other from two points that were 130 meters apart, at the same time. I did this so that their times would be the same, as we know that they will meet as some point, to make it easier with the Distance Speed Time calculations.

So we are asked what Jerry's distance will be from their meeting point once Tom reaches the house. So let's first find where their meeting point is. We now know that their time for the 130 meters distance was the same and we know the distance that each of them travelled would equate to 130. I expressed this as follows:

D1 = 2*t
D2 = 3*t
D1 + D2 = 130

2*t + 3*t = 130
5*t = 130 
t = 26

So now we know the time that each of them ran. So we can multiply it by any of their speeds, lets say Jerry, which would equal 26 * 2 = 52 meters, meaning Tom ran 78 meters.

We can now add the first 20 meters to Jerry's 52 meters and now we know where the middle point is. Jerry ran 72 meters and Tom ran 78 meters.

The next part of the question asks how far Jerry will be from this meeting point at the time Tom reaches the house. So we know that whatever time it takes Tom to get to the house can be multiplied by Jerry's speed to get his distance travelled.

Tom travels at 3 meters per second and needs to cover 72 meters, meaning it will take him 24 seconds to reach the house.

Now we can multiply 24 seconds by Jerry's speed of 2 meters per second to get 48 meters. Therefore, Jerry's distance will be 48 meters from the meeting point when Tom reaches the house.

The answer is D

pianogirl · Answer

After 10 seconds, Tom starts running and the distance between him and Jerry, who already started running, is 130 meters.

The two meet after  \frac{distance}{relative\ speed}

Since the two are running towards each others, their relative speed is the sum of the two speeds :
 relative\ speed = 2 + 3 = 5\ m/s

So it will take  \frac{130}{5} = 26\ s   for Tom and Jerry to meet after Tom starts running. At 26 seconds Tom will be  26*3 = 78\ meters  away from the barn and he still needs to run for  150-78= 72\ meters  to reach the house which will take him 24 seconds.

Therefore Jerry will be  2*24=48\ meters  away from their meeting point.

The right answer is  D

xrafael.juniorx · Answer

J and T start in opposition directions and are 150m apart.
(1) J runs 20m (2m/s * 10s). Then, T starts to run.
(2) They will meet when their combined speed reaches 130m (150m distance minus 20 run by J).
(2m/s+3m/s)*time = 130m > time = 130 / 5 = 26s.
(3) After 26 seconds, J run 20m + 2*26s = 72m, while T run 78m. 
(4) Due to the above, T will reach the house before J reaches the barn. T needs to run 72m, and considering 3m/s as his speed, this translates to 24s.
(5) J runs more 24s at 2m/s, which is equal to 48m from the point they crossed.

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