Jill and Matt run on a 400-meter-long oval track. They each run 10 laps daily and both run in the same lane. One day, they begin at the same point, but ran in opposite directions. Jill ran at a constant speed that was 2 meters per second faster than Matt's constant speed. Jill passed Matt for the first time in 40 seconds. Jill ran at a constant rate of how many meters per second?

Question

Jill and Matt run on a 400-meter-long oval track. They each run 10 laps daily and both run in the same lane. One day, they begin at the same point, but ran in opposite directions. Jill ran at a constant speed that was 2 meters per second faster than Matt's constant speed. Jill passed Matt for the first time in 40 seconds. Jill ran at a constant rate of how many meters per second?

Thanks in advance.

Answer 1

Jill distance = x

Matt distance = (400-x)
Jill speed = j
Matt speed = (j-2)

distance = rate * time
x = j (40)
(400-x) = (j-2)(40)
so
(400 -40 j) = 40 j - 80
I guess you can do it from there.

Answer 2

Let's assume Matt's constant speed is "x" meters per second.

Jill's constant speed is 2 meters per second faster than Matt's, so Jill's constant speed is (x + 2) meters per second.

Since Jill takes 40 seconds to pass Matt for the first time, we can set up the equation:
40(x + 2) = 400

Now we can solve for x:

40x + 80 = 400

Subtract 80 from both sides:

40x = 320

Divide both sides by 40:

x = 8

Therefore, Matt's constant speed is 8 meters per second.

To find Jill's constant speed, we can substitute the value of x into Jill's speed equation: (x + 2) = (8 + 2) = 10 meters per second.

So, Jill ran at a constant rate of 10 meters per second.

Answer 3

To find Jill's speed, we can use the concept of relative speed.

Let's assume Matt's speed is x meters per second. Since Jill's speed is 2 meters per second faster than Matt's, her speed would be (x + 2) meters per second.

We know that Jill passed Matt for the first time in 40 seconds. In this time, Jill would have covered a distance equal to the sum of their speeds.

The distance Jill covered in 40 seconds can be calculated by multiplying her speed by the time, which gives us (40 * (x + 2)). Similarly, Matt's distance can be calculated by multiplying his speed by the same time, which gives us (40 * x).

Since they started at the same point and ran in opposite directions, the sum of their distances should be equal to the total length of the track, which is 400 meters. Therefore, we can write the equation:

40 * (x + 2) + 40 * x = 400.

Now, we can solve this equation to find the value of x, which represents Matt's speed.