Question: Jerry and Jim run a race of 2000 m. First, Jerry gives Jim a start of 200m and beats him by 30 seconds. Next, Jerry gives Jim a start of 3mins and is beaten by 1000m. Find the time in minutes in which Jerry and Jim can run the race separately?

1. 8,10
2. 4,5
3. 5,9
4. 6,9
5. 7,10

Correct Answer: B
Solution and Explanation:
Approach Solution 1:

The problem statement states that:

Given:

• Jerry and Jim run a race of 2000 m.
• First, Jerry gives Jim a start of 200m and beats him by 30 seconds.
• Next, Jerry gives Jim a start of 3mins and is beaten by 1000m.

Find out:

• The time in minutes in which Jerry and Jim can run the race separately.

Jerry gives Jim a head start of 200 m. This implies that Jim begins not from the starting point but from 200 m ahead.
Jerry still beats him by 30 sec. This indicates that Jerry finishes the race whereas Jim takes another 30 sec to finish it.

In this race, Jerry covers 2000m.
At the same time, Jim covers the distance shown by the red line.
Jim requires another 30 sec ( i.e. 1/2 min) to cover the distance. Therefore he has not travelled the green line distance which is (1/2)*s where s is the speed of Jim. The distance Jim has actually covered at the same time as Jerry is [1800 - (1/2)*s] indicated by the red line.

Jerry gives Jim a start of 3 mins. This implies Jim begins running first while Jerry sits at the starting point.
After 3 mins, Jerry begins to run too.
Now, Jim beats Jerry by 1000 m. This implies that Jim reaches the end point whereas Jerry is still 1000 m away from the end.

In this race, Jerry covers a distance of 1000 m only.
In that time, Jim covers the distance shown by the red line (the distance before that Jim covered in the first 3 mins).
This distance shown by the red line is given by 2000 - 3s (3s is the distance covered by Jim in 3 minutes)

Now in the first race, Jerry covers 2000m while in the second race, he covers only 1000m.
Therefore in the second race, he must have run for only half the time.
Hence, in half the time, Jim would also have covered half the previous distance i.e. the second red line will be half the first red line.

Therefore, First red line = 2*second red line
1800 - (1/2)s = 2*(2000 - 3s) (where s is the speed of Jim in m/min)
s = 400 m/min

Time taken by Jim to run a 2000 m race = 2000/400 = 5 min.
Therefore, the answer is option B
Hence, the time in which Jerry and Jim can run the race separately is 4 min and 5 min respectively.

Approach Solution 2:

The problem statement informs that:

Given:

• Jerry and Jim run a race of 2000 m.
• First, Jerry gives Jim a start of 200m and beats him by 30 seconds.
• Next, Jerry gives Jim a start of 3mins and is beaten by 1000m.

Find out:

• The time in minutes in which Jerry and Jim can run the race separately.

Let’s solve the problem by using an intuitive method.
By analyzing the problem statement carefully, we can learn:
In the second instance, Jerry covers only half the distance (1000 m)
On the other hand, Jim covers the full distance (2000m) with 3 minutes extra

Let the time taken for Jerry to cover half the distance be x.
Hence, the time taken for Jerry to cover the distance full will be 2x.
Therefore, the time taken for Jim to cover the full distance = x + 3

Hence, the answer choice must be in the form of (2x, x+3).

Now let’s analyse the options:

1. 8,10 => 2*4 = 8, 4+3 ≠ 10, therefore, it does not satisfy the format (2x, x+3)
2. 4,5 => 2*2 = 4, 2+3 = 5, hence, this option satisfy the format (2x, x+3)
3. 5,9 => 5 is not a multiple of 2. Hence, the option gets eliminated.
4. 6,9 => 2*3 = 6, 3+3 ≠ 9, therefore, it does not satisfy the format (2x, x+3)
5. 7,10 => 7 is not a multiple of 2. Hence, the option gets eliminated.

Therefore, option B is the only choice that satisfies the format (2x, x+3) accurately.
Hence, the time in which Jerry and Jim can run the race separately is 4 min and 5 min respectively.

Approach Solution 3:

The problem statement indicates that:

Given:

• Jerry and Jim run a race of 2000 m.
• First, Jerry gives Jim a start of 200m and beats him by 30 seconds.
• Next, Jerry gives Jim a start of 3mins and is beaten by 1000m.

Find out:

• The time in minutes in which Jerry and Jim can run the race separately.

Let, Jim's speed is X m/min
Let, Jerry's speed is Y m/min

The question states that Jerry gives Jim a start of 200m and beats him by 30 seconds.
Let’s create an equation with respect to the time taken by both;

1800/X - 2000/Y = 0.5
1800Y - 2000X = 0.5XY
3600Y - 4000X = XY .....(1)

The question states that Jerry gives Jim a start of 3 mins and is beaten by 1000m
Let’s create an equation with respect to the time taken by both;
2000/X - 1000/Y = 3
2000Y - 1000X = 3XY .....(2)

Now let’s solve both equations (1) and (2):
=> 3(3600Y - 4000X) = 2000Y - 1000X
=> 10800Y - 12000X = 2000Y - 1000X
=> 108Y - 120X = 20Y - 10X
=> 88Y = 110X
=> 8Y = 10X
=> X/Y = 4/5

The speeds of Jim and Jerry are in the ratio of 4:5.
Therefore, the ratio of their time will be 5:4
This implies that Jim would take 5 mins and Jerry would take 4 mins.

Hence, the time in which Jerry and Jim can run the race separately is 4 min and 5 min respectively.

“Jerry and Jim run a race of 2000 m. First, Jerry gives Jim”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. The candidates should analyse the data and calculate effectively in order to solve GMAT Problem Solving questions. The candidates can practice different varieties of questions from the GMAT Quant practice papers that will help them to further improve their mathematical knowledge.

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