Question

Pallavi beats Anuva in a kilometre race by 50 s and
Richa by 450 m. If Anuva and Richa run a kilometre
race, Anuva wins by 40 s. How much time does Richa
take to run a kilometre?​

Answer 1

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Pallavi beats Anuva in a kilometre race by 50 s and

Richa by 450 m. If Anuva and Richa run a kilometre

race, Anuva wins by 40 s. How much time does Richa

take to run a kilometre?

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Given:-

A beats B by 50 sec.

Means A reached finish point 50 sec earlier than B(or B takes 50 sec more to complete the race) in one kilometer race.

Hence Time req for B - Time req for A = 50sec

DBSB−DASA=50 sec

1000SB−1000SA=50 sec -------------(1)

Now, A beats C by 450 m. (Means when A reaches finish line, C is 450 meters behind him)

Means in the same time A reaches 1000m (race is KM race) and C reaches 550m

DASA=DCSC (Equating their times)

1000SA=550SC ------------------(2)

Now B beats C by 40s. Means C takes 40s more to reach finish line

hence Time req for C - Time req for B = 40sec

DCSC−DBSB=40 sec

1000SC−1000SB=40 sec --------------(3)

Now by Adding equation 1 and 3

1000SC−1000SA=90 sec ---------------(4)

Substitute 2 in equation 4

1000SC−550SC=90 sec

450SC=90 sec

Sc = 5 m/s

Hence, time to reach 1 KM = 1000m5m/sec=200sec

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