Lead in a race

[kartikshah]

In a 100m race, Sam beats John by 4 seconds. On the contrary, if Sam allowed John to start 16m ahead of Sam, then Sam and John reach the finishing point at the same time. How long does Sam take to run the 100m race?

A. 4 seconds

B. 25 seconds

C. 29 seconds

D. 21 seconds

E. 6.25 seconds


Please help with this question.

I don't understand complex RTD questions. Is there a simpler approach to them? I know how to solve the following types with ease:

(a) Simple RTD
(b) Two objects in same direction (time taken to catch up questions)
(c) Two objects in opposite direction (distance apart questions)

But not those questions like the one above!!

[Birottam Dutta]

See,

When Sam allows for a 16 m head start he and john reach at the same time, so Sam requires the 4 seconds to cover this additional 16m.

Hence, speed of Sam = 16/4 = 4 m/s.

Therefore, time taken by Sam to run the 100m race = 100/4 = 25 seconds.

Answer = B!

[kartikshah]

Huh!
It was this simple?!!
I really need to shed my prejudice for RTD problems :-)

[optimist]

I am getting 21 (C) as the answer, please see if am doing anything wrong

Let time taken by Sam to cover 100m be 't' ==> Sam's speed = 100/t
therefore, time taken by John = t+4 ==> John's speed = 100/(t+4)

Now, since John starts 16 m ahead of Sam,
time taken by Sam to cover 100m = time taken by John to cover 84m:

==> 100/100*t = 84*(t+4)/100
on solving, t = 21

please help

[eagleeye]

I am getting 21 (C) as the answer, please see if am doing anything wrong

Let time taken by Sam to cover 100m be 't' ==> Sam's speed = 100/t
therefore, time taken by John = t+4 ==> John's speed = 100/(t+4)

Now, since John starts 16 m ahead of Sam,
time taken by Sam to cover 100m = time taken by John to cover 84m:

==> 100/100*t = 84*(t+4)/100
on solving, t = 21

please help

Optimist you are right. The correct answer is D.

John covers the additional 16m in 4s. John's speed = 16/4 = 4m/s.
Time taken by John to run 84m = time taken by Sam to run 100m = 84/4 = 21 seconds.

Cheers!