John takes 20 min to walk every kilometer (km). David takes 16 min to

I am not sure if my answer is correct

speed of John-3km/hr
speed of David-3.75km/hr

when time is constant

D(David)=3*t
D(John)=3.75*t
when t=1
D(J)-D(D)=0.75km

for David to beat John by 0.75km it takes 3.75 km hence to beat by for 0.24km it will take 1.2km.and that will be length of the race as David is faster and he will reach the finish point first .IMO option B

Main Formula : D=RT
JOHN :
D = D-0.2 (240/1000)= 0.2
R = R
T = 20

D = RT
D-0.2 = 20R
D-0.2/20 = R --- 1)

Likewise for David
D=RT
D=D
R=R
T=16
Or , D = R16
Or, D = 16(D-0.2)/20 [From Equation 1]
Or D ~ 0.7

For JOHN D = 0.7 - 0.2 = 0.5

Total D = 0.7 + 0.5 = 1.2 Answer B

john=50m/min
david=62.5m/min
David beats john by 240 meters
Realtive speed=12.5meters/min
time taken to complete 240 meters=240/12.5 -->19.2 minutes(overall time of the race)
David walked for 19.2 minutes--> 19.2*62.5=1200 meters-->1.2km

BASIS OF SOLUTION:
The ratio of the speeds of two moving objects can be expressed in two ways:
(a) As the ratio of the respective distances they cover in any given time (e.g., if S1 and S2 are the speeds and D1 and D2 are the distances covered in any given time, then S1/S2=D1/D2)
(b) As the inverse of the ratio of the time taken by each to cover any given distance (again, if S1 and S2 are the speeds and T1 and T2 are the times taken to cover any given distance, S1/S2=T2/T1)

SOLUTION:
(a) Let X meters be the length of the race. In the time that David takes to cover X meters, John covers (X-240) meters. If SD and SJ are David's and John's speeds then:
SD/SJ=X/(X-240)
(b) David and John cover 1 km in 16 minutes and 20 minutes respectively. Therefore:
SD/SJ=20/16
Thus, X/(X-240)=20/16
X=1200 meters=1.2 kms. ANS: B

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.