Question

In a 5000 m race, the athletes run 12 1/2 laps; each lap is 400 m.Kara runs the race at a constant pace and finishes in 17.9 min.Hannah runs the race in a blistering 15.3 min, so fast that she actually passes Kara during the race.How many laps has Hannah run when she passes Kara?

Answer 1

7 Laps

Step-by-step explanation:

Velocity = Displacement / Time

Velocity of Kara

`V_K=(5000)/(17.9* 60)`

Velocity of Hannah

`V_H=(5000)/(15.3* 60)`

When Hannah will pass Kara they both would have run the same amount of time.

Displacement = Velocity × Time

`400=(V_H-V_K)T\\\Rightarrow T=(400)/(V_H-V_K)\\\Rightarrow T=(400)/((5000)/(15.3* 60)-(5000)/(17.9* 60))\\\Rightarrow T=505.61\ s`

Distance = Speed × Time

`Distance=(5000)/(15.3* 60)* 505.61\\\Rightarrow Distance=2753.86\ m`

Distance traveled by Hannah

`(2753.86)/(400)=6.88\ Laps`

So, Hannah would have run 7 Laps when she passes Kara