Jerry and Jim Run a Race of 2000 M First Jerry Gives Jim a start of 200m GMAT Problem Solving

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.

Suggested GMAT Problem Solving Samples

• In isosceles triangle EFG above, angle FEG measures 60 degrees GMAT Problem Solving
• In the Figure, O is the Center of the Circle. Which One of the Following GMAT Problem Solving
• If a and b are Positive Integers and (2a)^b= 2^3, What is the Value GMAT Problem Solving
• What is the Remainder When 3^243 is Divided by 5? GMAT Problem Solving
• A Fashion Designer Sold a Pair of Jeans to a Retail Store for 40 Percent GMAT Problem Solving
• A Rectangular-Shaped Carpet Remnant That Measures x Feet GMAT Problem Solving
• In The Figure Above, If The Square Inscribed In The Circle Has An Area GMAT Problem Solving
• A Right Triangle Is Inscribed In A Circle. The Legs Of The Triangle GMAT Problem Solving
• Tom and Jerry are running on the same road towards each other. If Tom GMAT Problem Solving
• A number is said to be prime saturated if the product of all the different GMAT Problem Solving
• What is the sum of first 10 non-negative even integers GMAT Problem Solving
• A certain computer program randomly generates equation of line is form GMAT Problem Solving
• A perfect number is one which is equal to the sum of all its positive GMAT Problem Solving
• At A Prestigious Dog Show, Six Dogs Of Different Breeds Are To Be GMAT Problem Solving
• The Average Wages of a Worker During a Fortnight Comprising 15 GMAT Problem Solving
• Which of the Following Fractions is the Largest? GMAT Problem Solving
• Alice and Bob Traveled in the Same Direction Along the Same Route at GMAT Problem Solving
• Paul, Quallis and Robert Divide a Sum of Money Among Themselves in the GMAT Problem Solving
• If A Sphere With Radius r Is Inscribed In A Cube With Edges Of Length GMAT Problem Solving
• A Globe Of Radius 8 Inches Is To Be Placed Into A Square Box For Shipment GMAT Problem Solving
• What is the sum of digits in decimal notation of number (10^20) - 16? GMAT Problem Solving
• Which of the following is equivalent to the pair of GMAT Problem Solving
• A password to a certain database consists of digits that can GMAT Problem Solving
• A Can do 1/3 of the Work in 5 Days and B Can do 2/5 of the Work in 10 Days GMAT Problem Solving
• The income of a broker remains unchanged though the rate of commission is increased GMAT Problem Solving
• Curly Brackets {} Around the Last Digits of a Decimal Fraction Signify GMAT Problem Solving
• For the infinite sequence a1, a2, a3, ... an, an+1, an=3(an−1) for all GMAT Problem Solving
• The quantities S and T are positive and are related by the equation GMAT Problem Solving
• A child paints the six faces of a cube with six different GMAT Problem Solving
• In an opera theater. there are 300 seats available GMAT Problem Solving
• At the Rate of m Meters Per s Seconds, How Many Meters Does a Cyclist GMAT Problem Solving
• NASA Received Three Messages in a Strange Language From a Distant Planet GMAT Problem Solving
• Two Cyclists Start From the Same Place to Ride in the Same Direction GMAT Problem Solving
• A Sphere is Inscribed in a Cube with an Edge of 10. What is GMAT Problem Solving
• If AC = BC and CD = DE Then, in Terms of x, the Value of y is GMAT Problem Solving
• What Is The Units Digit Of The Product Of Any Five Consecutive Positive Integers GMAT Problem Solving
• A Large Cube Consists Of 125 Identical Small Cubes GMAT Problem Solving
• A Pizzeria Makes Pizzas That Are Shaped As Perfect Circles GMAT Problem Solving
• The Number Of Diagonals Of A Polygon Of n Sides Is Given By The Formula GMAT Problem Solving
• The Work Done By A Woman In 8 Hours Is Equal To The Work Done By A Man GMAT Problem Solving
• A Circle Is Inscribed Inside Right Triangle Abc Shown Above GMAT Problem Solving
• The Temperatures In Degrees Celsius Recorded At 6 In The Morning In GMAT Problem Solving
• A Truck Travelling At 70 Kilometres Per Hour Uses 30% More Diesel To GMAT Problem Solving
• If The Area Of A Rectangle Is Equal To The Area Of A Square, Then The GMAT Problem Solving
• The rectangles shown above are similar and the ratio of the area of GMAT Problem Solving
• A School has Set Different Minimum Qualifying Marks in an Exam GMAT Problem Solving
• The Temperature of Delhi and Lucknow were in the Ratio 3:5 in July GMAT Problem Solving
• When a Certain Tree was First Planted, it was 4 feet Tall and the Height GMAT Problem Solving
• When a Number A is Divided by 6, the Remainder is 3 and When Another GMAT Problem Solving
• Which of the Following is the Correct Ordering of 2√13, 4√3, 5√2 and 3√6 ? GMAT Problem Solving