Question

Friends Mercedes and Kaandra are working out together at the 400 m track. Kaandra can do the 1600 m in a blazing 5 minutes and 30 seconds. Mercedes is significantly slower doing that distance in 7 minutes. The women decide to have a race going twice around the track. To make it more competitive Kaandra gives Mercedes a 100 m head start (i.e. Mercedes only runs 700 m). Who wins, by how much time?

Answer 1

Step 1: Find average running speed of both friends:

V1 = speed of Kaandra = distance/time taken

1600 m in 5 min 30 sec, So d = 1600 m , and t = 330 sec

V1 = 1600/330 m/s = 4.85 m/s

V2 = speed of Mercedes = distance/time taken

1600 m in 7 min, So d = 1600 m , and t = 420 sec

V2 = 1600/420 m/s = 3.81 m/s

Step 2: Now calculate time taken by both to complete the race going twice around the track

given that track is 400 m, so in two round they will race for 800 m

time taken by Kaandra to complete the race will be

t1 = distance/Speed

since Kaandra travels total 800 m, So

t1= 800 m/(4.85 m/s) = 165 sec (approx)

time taken by Mercedes to complete the race will be

t2 = distance/Speed

since Mercedes travels only 700 m (as 100 m head start is given), So

t2 = 700 m/(3.81 m/s) = 184 sec (approx)

So we can see that t2 > t1

That means Kaandra wins the race.

time = t2 - t1 = 184 - 165 = 19 sec

Kaandra wins the race by approximately 19 sec (which is greater than 10 sec)