In a 100m race, Sam beats John by 4 seconds. On the contrary

One more approach:

(Distance x time) of Sam = (Distance x time) of John
************************************************

Distance travelled by Sam = 100
Time taken by Sam = t


Distance travelled by John = 100-16 = 84
Time taken by John = t+4


84 (t+4) = 100 (t)

Solving this, t= 21

D. 21 second

100/Vj - 100/Vs = 4 ----(1)
100/Vs = 84/Vj = 21 ----(2)
solve these 2 equations , Vj=4

Ts = 100/Vs ----> solve from 1st equation , Ts = 21

Good Approach. I got D too by solving 2 equations and I took 1 min. Your approach probably saves atleast 30 more secs.

Their difference is 4 second but this difference is 0 if john allows Sam to start the race from 16m ahead . that means Jhon was 16m away from finishing line when they started together . so He will cover 16 m in 4 seconds . so his speed =16/4=4 metre / second . so time taken =100/4=25 seconds . so Sam took = 21 seconds .

correct answer = D

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arranging info into rtd chart suggested by mgmat is really helpful.

plug (3) into (2) and you receive Jonh's speed of 4 m/sec. So John takes 25 seconds to make 100 meters and Sam takes 4 secs less = 21.

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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?

I tried solving out using formulas but I did it out in my head instead.

If Sam allowed John to start out 16m ahead and they finished the race at the same time, while John lost to Sam in the last race by 4 seconds, this means John runs at 16m a second. If John were to start ahead of Sam by this 16m distance and they finished the race at the same time, John would have completed the race in 25 seconds. However, Sam is faster than John and closes the 4 second, 16 meter gap. Sam would have had to spend less time running than John for them to finish the race at the same time, the four seconds that John needed beat Sam.

D. 21 seconds

I wouldn't say that he had to run 'those' first 16m in 4 seconds but that in total we would have to run an extra 16m whatever they are in the whole track so that it can account for that 4 extra seconds.

The rest is very good

Cheers!
J

T=Sam's time
100/(T+4)=John's rate in race 1
84/T=John's rate in race 2
100/(T+4)=84/T
T=21 seconds

took some time to think about how to solve this one...
so John takes 4 seconds more to run the remaining 16 meters. so 16/4 = 4m/s is the speed of John.
john runs 100 meters in 25 seconds.
we know that sam needs 25-4 =21 seconds.

D.

Given: Sam gives John a start of 16 m and they reach at the same time
It implies that when John covers 84 m, Sam covers 100 m in the same time
Therefore, their speed will be in the ratio of 84 to 100 and time taken will be in the ratio of 100 to 84
Reducing the ratio of time we get, 21 to 25 which gives that difference of 4 seconds.
Therefore, the time taken by Sam is 21 seconds.

Since distance is the same in the first case, first equation is s1/s2=t2/t1
Since time is the same in the second case, second equation is s1/s2= d1/d2
Therefore, d1/d2=t2/t1
84/100=(t-4)/t
t=25,
t-4=21 seconds

That 16m lead exactly offsets the 4 second difference between them. Sam still runs the same time; John is saving 4 seconds and 16m. 16m:4sec is 4m/sec. That is how fast John runs.

If we go back to the initial scenario in the question and have them both do the full 100m, John does it in 100/4 = 25 seconds. Sam is 4 seconds faster, so 21 seconds.

Answer choice D.

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