If I walk at 4 km/hr, I miss the bus by 10 minutes. If I walk at 5 km/

10min = 1/6
5min = 1/12

4(t+1/6) = 5(t-1/12)
13/12 = t

4(13/12+1/6) = 4(15/12) = 15/3 = 5

Here, with respect to the Time Speed and Distance Problems - The basic equation that is important is => Distance=Speed*time.

Here let the distance be X. It is going to be X for both the cases as the distance from the point to the bus-stop is the same.

First Case = If he walks at the speed of 4Kms per hour = He takes 10 Mins Extra.

Second Case = If he walks at the speed of 5kms per hour = He takes 5 Minutes less.

Hence, if he is going to increase the speed by 1 km/hr, he gains 15 minutes.

So the Equation will be as follows :

(X/4) - (X/5) = 15/60.

This way, if you reduce the equation we get the below mentioned simplified equation :

(5X-4X)/20=15/60.

Solving for the same, we get X = 5.

Hence the Answer for the above mentioned question is A


K S Raksha
GMAT Tutor at Wizako GMAT Classes & Online Courses

This question can be solved quite easily if we apply the proportionalities between Time, Distance and Speed.

When distance is constant, time is inversely proportional to time. This means, if Distance is constant, \(\frac{S_1}{S_2} = \frac{T_2}{T_1}\).

Let \(S_1\) = 4 km/hr and \(S_2\) = 5 km/hr. Then, \(\frac{T_2}{T_1}\) = 4/5. This means that \(T_2\) = \((\frac{4}{5}) T_1\); so time saved = \((\frac{1}{5})T_1\).

But, the person saved 15 minutes by walking faster in the second case. Therefore,

\((\frac{1}{5}) T_1\) = 15 or \(T_1\) = 75 minutes or \(T_1\) = 1 ¼ hours.

Distance = Speed * Time.

Therefore, the distance to be covered to reach the bus stop = 4 km/hr * 1 ¼ hours = 5 km.
The correct answer option is A.

Note: The bus arrives at the 65th minute, that’s why in the first case the person missed the bus by 10 minutes since he takes 75 minutes to reach the bus stop; similarly in the second case, the person is 5 minutes early since he takes exactly 60 minutes to reach the bus stop. Just a quick way of checking your answer.

Hope that helps!

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