Walking at 3/4 of his Normal Speed, Mike is 16 minutes Late GMAT Problem Solving

Question: Walking at 3/4 of his normal speed, Mike is 16 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and his office is

1. 42 minutes
2. 48 minutes
3. 60 minutes
4. 62 minutes
5. 66 minutes

“Walking at 3/4 of his normal speed, Mike is 16 minutes late”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:
Approach Solution 1

We can let r = Mike’s normal speed and t = the time he normally takes to reach his office from home. Thus, the distance between his home and his office is rt.

Since we are given that he is 16 minutes late in reaching his office when he walks at 3/4 of his normal speed, we can say that his new speed = (3/4)r and his new time = t + 16. Thus, the distance between his home and his office, in terms of the new speed and new time, is (3/4)r(t + 16).

Since the distance between his home and his office doesn’t change in relation to speed and time, we have:

rt = (3/4)r(t + 16)
Divide both sides by r, we have:
t = (3/4)t + 12
(1/4)t = 12
t = 48

Correct Answer: B

Approach Solution 2

Let's start with a word equation

Distance travelled at 3/4 speed = Distance travelled at regular speed
Let v = regular walking speed (in miles/minute)

So, 3v/4 = REDUCED walking speed (in miles/minute)

Let t = regular travel time (in minutes)
So, t + 16 = travel time (in minutes) when walking 3/4 speed
Distance = (speed)(time)

So, we get: (3v/4)(t + 16) = vt

Expand: 3vt/4 + 12v = vt
Multiply both sides by 4 to get: 3vt + 48v = 4vt
Subtract 3vt from both sides: 48v = vt

Rewrite as: vt - 48v = 0
Factor: v(t - 48) = 0

So, EITHER v = 0 PR t = 48

Since the speed (v) cannot be zero, it must be the case that t = 48

Correct Answer: B

Approach Solution 3

Let the distance between home & office be ‘D’ and his normal speed be 'x'.

Mike usually takes (D/X) minutes or hours to reach the office from home. This is what we need to find.

His new rate is 3x/4 so the time it takes is D/(3x/4) = 4D/3x

It says travelling at his new rate, he is 16 minutes late so

--> 4D/3x - D/x = 16 minutes
--> 4D-3D/3x = 16 minutes
--> D/3x = 16 minutes
--> D/x = 48 minutes

Correct Answer: B

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