Walking at 6/7 th of His Usual Speed, a Man is 25 Min Too Late GMAT Problem Solving

Question: Walking at 6/7 th of his usual speed, a man is 25 min too late. His usual time is

1. 1 1/2 h
2. 2 1/2 h
3. 2 3/4 h
4. 2 4/5 h
5. 3 h

Correct Answer: B

Solutiion and Explanation
Approach Solution 1:

A man is 12 minutes late if he walks at 6/7ths of his normal speed.

It is necessary to determine how long it typically takes him to travel that distance.

Let x represent the distance traveled.

Let y be the original speed.

Time = Distance/speed

The original time taken is time = x/y

Walking 6/7th of his usual speed.

i.e. new speed is 6/7y

New time is x/(6/7)y

Time = 7x/6y

A man is 25 minutes too late.

New time – Original time = 25

7x/6y = x/y = 25

x/y (7/6 -1) = 25

x/y = 25*6

= 150

The usual time taken by him to cover the distance is 150 minutes or 2 hour 30 minutes.

Approach Solution 2:

It is known that-

Speed ∝ \(\frac{1}{time}\)

Let, his normal speed be x. If his speed is x, time taken will be 1/x, now his speed is 6x/7 then the time taken will be 7x/6.

In this case, late time~usual time = 25 minute

So, 7x/6~x=25

=>x=150 minute.

or 2 hour 30 minutes.

Approach Solution 3:
We can let r be his usual speed and t be his usual time. We can create the equation:

rt = (6r/7)(t + 25/60)

rt = 6rt/7 + 25r/70

rt/7 = 25r/70

t/7 = 5/14

t = 5/14 * 7 = 5/2 = 2 ½ hours

“Walking at 6/7 th of his usual speed, a man is 25 min too late”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
 

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