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

Question

If I walk at 4 km/hr, I miss the bus by 10 minutes. If I walk at 5 km/hr, I reach 5 minutes before the arrival of the bus. How far should I walk to reach the bus stand?

(A) 5 km 
(B) 10 km 
(C) 15 km 
(D) 20 km
(E) 25 km

GMATinsight · Answer

Distance = Speed * Time

Let, Normal Speed = S km/hr
Normal Time = T minutes

now, Distance = S*T = 4*(T+10) = 5*(T-5)

i.e. (T+10)/(T-5) = 5/4

i.e. 4T + 40 = 5T - 25

i.e. T = 65 minutes

i.e. Distance = 5*(T-5) = 5*(65-50)/60 = 5 km . (converting minutes into hour by dividing (65-5) by 60)

Answer: Option A

Archit3110 · Answer

we can solve this considering relation that distance to bus stand is same at both times
so
speed = s kmph and time = t
4*(t+10)=5*(t-5)
t+10/t+5=5/4
solve for t = 65 mins ; 65/60 hrs

distance = 4 * (t+10) = 4* 75 /60 = 5 kms
IMO A

fireagablast · Answer

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

wizakoraksha · Answer

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

CrackverbalGMAT · Answer

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!

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards