The Speed Of A Car Increases By 2 Kms After Every One Hour GMAT Problem Solving

Question: The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 35 kms. What was the total distance travelled in 12 hours?

A) 456 km
B) 482 km
C) 552 km
D) 556 km
E) 345 km

“The speed of a car increases by 2 kms after every one hour”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT quant section analyses the analytical and logical knowledge of the students to solve critical mathematical problems. The students must determine the appropriate option by calculating it with reasonable mathematical skills. The students must know about qualitative facts in order to solve GMAT Problem Solving questions. The GMAT Quant topic in the problem-solving part consists of calculative mathematical problems that should be solved with better mathematical concepts.

Solution and Explanation:

Approach Solution 1:

The problem statement informs that:

Given:

  • The speed of a car increases by 2 kms after every one hour.
  • The distance traveled in the first one hour was 35 kms.

Find Out:

  • the total distance travelled in 12 hours

Speed in the first hour = distance/ time = 35 kmph (since the distance travelled in first one hour = 35 kms)

Speed in every one hour is 2 kms more than the previous speed overcome.
Therefore, the range of speed will be 37 kmph, 39 kmph ….
Therefore, the total distance traversed in 12 hrs will be the aggregate of distances covered in individual 12 hrs:
35 + 37 + 39 + 41 + … and so on.
Sum = (n/2)* [2a + (n - 1)* d]

=> Sum = (12/2)* [2* 35 + (12 - 1)* 2]
=> Sum = 6 * [70 + 22]
=> Sum = 552 km,

Therefore, the total distance travelled in 12 hours = 552 km

Correct Answer: (C)

Approach Solution 2:

The problem statement indicates that:

Given:

  • The speed of a car rises by 2 kms after every one hour.
  • The distance traversed in the first one hour was 35 kms.

Find Out:

  • the total distance travelled in 12 hours

As per the question, the total distance travelled in 12 hours = Sum of A.P series
Therefore, according to the formula, Sum of A.P series = n/2[2a + (n − 1) × d], where a= first term, d= common difference, n= number of terms.
Here, the question states that a= 35, d=2, and n=12, that is we can say,
The total distance travelled in 12 hours = 12/2 ∗[2∗35+(12−1)2]
                                                               =6[70+22] 
                                                                =552 kms.

Correct Answer: (C)

Approach Solution 3:

The problem statement specifies that:

Given:

  • The speed of a car rises by 2 kms after every one hour.
  • The distance traversed in the first one hour was 35 kms.

Asked:

  • Find the total distance travelled in 12 hours

Since the speed of the car increased by 2 km in every subsequent hour and the total time taken by the car is 12 hours, then we can say:
The distance travelled by car will start from 35 and will end at 57.
The distance travelled by car in individual hours = 35 + 37 + 39 + 41 + 43 + 45 + 47 + 49 + 51 + 53 + 55 + 57
It can be analysed that there exist five such pairs, whose sums up to 90.
35 + 55 = 37 + 53 = 39 + 51 = 41 + 49 = 43 + 47 = 90
Therefore, the sum of the total distance travelled by car is 90*5 + 45 + 57

= 495 + 57
= 552 kms.
Thus, the total distance travelled in 12 hours = 552 kms

Correct Answer: (C)

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