SOLUTION: In a kilometer race, If Abhishek gives Bharti a 40m start, Abhishek wins by 19sec. But if Abhishek gives Bharti a 30 sec start, Bharti wins by 40 m. Find the time taken by Bharti t

Question 857986: In a kilometer race, If Abhishek gives Bharti a 40m start, Abhishek wins by 19sec. But if Abhishek gives Bharti a 30 sec start, Bharti wins by 40 m. Find the time taken by Bharti to run 5,000m?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
it took me a while but i finally figured it out.
the solution is:
Abhishek runs at 8 meters per second.
Bharti runs at 20/3 meters per second.
the formula is rate * time = distance.
the distance that bharti runs is 5000 meters.
his rate of speed is 20/3 meters per second.
time = distance / rate so:
the time it will take him to run 5000 meters is 5000 / (20/3) = 750 seconds.

first we'll see if the rates of speed make sense.
a kilometer race is equal to 1000 meters.

if Abhishek gives Bharti a 40 meter start, then Abishek is running 1000 meter and Bharti is running 960 meters.
Assuming that Abishek runs 1000 meters in T-19 seconds, then the rate of speed that Abishek is running is (1000 / (T-19)) meters per second.
Assuming that Bharti runs 960 meters in T seconds, then the rate of speed that Bharti is runnins is (960 / T) meters per second.

The one constant in all of this is the rate of speed that Abishek is running and the rate of speed that Bharti is running.

Those numbers are, once again:

RA = Abishek rate of speed = (1000 / (T-19)) meters per second.
RB = Bharti rate of speed = (960 / T) meters per second.

Now we look at the second part of the problem.

If Abhishek gives Bharti a 30 second start, Bharti wins by 40 meters.
This means that Bharti is running 1000 meters in (x + 30) seconds while Abishek is running 960 meters in x seconds.

Since rate * tine = distance, then time = distance / rate.

Bharti is running 1000 meters at a rate of speed of (960 / T) meters per second, so the time that Bharti is taking is equal to 1000 / (960 / T) which is equal to (1000 * T) / 960.

Abishek is running 960 meters at a rate of speed of (1000 / (T - 19)) meters per second, so the time that Abishek is taking is equal to 960 / (1000 / (T - 19)) which is equal to (960 * (T - 19)) / 1000).

So we have 2 times for the second run.

The time for Bharti is equal to (1000 * T) / 960.

The time for Abishek is equal to (960 * (T - 19)) / 1000.

Now Abishek gave Bharti a 30 second head start, so Bharti's time is equal to Abishek's time + 30 seconds.

you get the formula:

(1000 * T) / 960 = (960 * (T - 19)) / 1000 + 30

Solve this formula for T to get T = 144 seconds.

That solve the problem, because once you know T, everything else falls into place.

The attached picture shows my calculations for solving that equation.

$$$

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