Catniss is runs the first lap of a race at a speed of 10m/s. The second lap she changes speed, and takes 40 seconds in this lap. Determine the speed she needs to go in the second lap in order to achieve an overall speed of 20m/s with an overall time of 60 seconds.

The first lap is run at a speed of 10 m/s
Time to cover the first lap is not given, let us indicate it as t1
Distance covered = speed x time = 10 x t1 = 10t1

The second lap is covered in 40 seconds. The speed is not given, let us
Distance covered in second lap = s2 x 40 = 40s2

Total time taken to cover both laps = t1 + t2 = 60 seconds
We know t2 = 40 seconds so t1 = 60 - 40 = 20 seconds
So the distance covered in the first lap = 10 x 20 = 200 meters

The total distance covered = st where s is the overall speed and t is the overall time

If overall speed of 20 m/s is achieved in 60 s, the overall distance covered must be 20 x 60 = 1200 meters

That means the distance for the second lap = 1200 - distance for first lap = 1200 - 200 = 1000 meters

Since Catniss covers this second lap distance of 1000 meters in 40 seconds, that means her second lap speed = distance/time
= 1000/40 = 25 m/s

yidan0201 yidan0201 · Answer 2 · 2024-01-17T12:06:08+01:00

Step-by-step explanation:

let's break down the problem step by step in the first step can it runs at a speed of 10 miles per second for an unknown distance let's call this distance D1 and the second lab she changes her speed to and text 40 seconds to complete the lap let's call her speed in the second lap S2 and a distance she covers in the second lap D2,

we know that her overall speed is 20 minutes per second and she completes the entire race in 60 seconds so we can write the following equations

1. d1/10 + d2/s2 = 60 (time taken for the entire race is 60 Seconds)

2. D1 + D2 equals total distance of the race, which is unknown

we need to find the value of S2

for the first equation we can express D1 in terms of D2

D1 = 600 - (40 * S2)

now we subtitle do you want in terms of D2 into the second equation 600 - (40 * S2) + D2 = total distance of the race

now we can solve this for D2

D2 equals total distance of for the race - 600 + (40 * s2)

now we can subtitle data back into the first equation (600 - (40 * S2)) / 10 + D2 / S2 = 60

rearrange the equation

(40S2 - 4S2 + total distance of rice - 600) /x2 = 0

combine like terms

(36S2 + total distance of the race - 600) / S2 = 0

multiply both sides by S2

36s2 + total distance of race- 600 = 0

rearrange the equation to solve for S2

36s2 = 600 - total distance of phrase

S2 = (600 - total distance of the race) /36

now we know that in order to achieve an overall speed of 20 m/s with an overall time of 60 seconds catnip needs to run the second half at the speed of (600 - total distance of the race) /36m/s

I hope this helps I used a little AI catnip needs to run the second Lab at the speed of 600 - total distance of the race/36/s