A Man walked from his house to office at 5kmph and got 20 mi

Question

A Man walked from his house to office at 5kmph and got 20 minutes late. if he had travelled at 7.5kmph, he would have reached 12 minutes early. The distance from his house to office is?

A) 4Km
B) 16Km
C) 8Km
D) 9Km
E) 12Km

fameatop · Accepted Answer

Let the original distance and time be D & t
 Case 1  - If man travels at 5kmph, he reaches late 20 min or 1/3 hr
We can write the same as 
 \frac{D}{5}  = t +  \frac{1}{3}  -----(1)

Case 2  - If man travels at 7.5kmph, he reaches early 12 min or 1/5 hr
We can write the same as 
 \frac{D}{7.5}  = t -  \frac{1}{5}  -----(2)

Solving both we get D = 8
Answer C

Bunuel · Answer

Discussed here: time-speed-and-distance-simplified-150163.html

SVaidyaraman · Answer

1 Distance traveled is the same in both the cases
2 5 * (t + 1/3) = 7.5 * (t- 1/5) 
3 t=19/15 hrs
4 Substituting the value of t in the LHS of (2), Distance = 5 *( 19/15 +1/3) = 8 km 
 
Substituting the value of t in RHS of (2) will also give the same answer

jlgdr · Answer

I'm not sure if this method is valid but please comment

d/5 = t+20
d/7.5 = t-12

So 5t + 100 = 7.5t - 90

t = (190)(2)/5 = 78

So distance (78)(5) + 100 /60

C

I divided by 60 to go back to hours cause I was working with minutes before

Hope it helps
Cheers!
J

noTh1ng · Answer

I did it the same way, however t = (190*2)/5 should read = 76 not 78.

(76*5 + 100) / 60 = 8

Abhishek009 · Answer

Distance is constant

\frac{5* ( t + 20 )}{60} = \frac{( t - 12 )*30}{4*60}

20( t + 20 ) = ( t - 12 )30

20t + 400 = 30t - 360

760 = 10t

So,  t = 76

Thus distance =  \frac{5( 76 + 20 )}{60}

Hence distace = 8 km
  
Answer will be (C) 8 Km

gracie · Answer

d/5-8/15=d/7.5
d=8 km

GMATGuruNY · Answer

Rate and time have a RECIPROCAL RELATIONSHIP.
As a result:
If the same distance is traveled at two different speeds, THE RATE RATIO is equal to THE RECIPROCAL OF THE TIME RATIO.

Rate ratio:
Since the first trip is traveled at 5kph, while the second is traveled at 7.5kph, we get:
 \frac{first-rate}{second-rate} =   \frac{5}{7.5} = \frac{10}{15} = \frac{2}{3}

Time ratio:
Since the time for the second trip is 32 minutes less than the time for the first, we get:
 \frac{first-time}{second-time} =   \frac{t}{t-32}

Since the rate ratio is equal to the reciprocal of the time ratio:
 \frac{2}{3} = \frac{t-32}{t} 
 3t-96=2t 
 t =  96 minutes  = \frac{96}{60}  hours  = \frac{8}{5}  hours

Since the trip traveled at 5kph takes  \frac{8}{5}  hours, we get:
 d = rt = 5*\frac{8}{5} = 8  kilometers

C

hero_with_1000_faces · Answer

I usually use the formula

(Speed1*speed2)* time difference ÷ speed1-speed 2

Hence 5*7.5*32/2.5*60

60 coz we need answer in hours

Hence 8

Posted from my mobile device

bumpbot · Answer

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A Man walked from his house to office at 5kmph and got 20 mi

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