Jess is running around a circular track, one lap every 40 seconds. Mackenzie is also running at a constant speed around the same track, but in the opposite direction. They meet every 15 seconds. How many seconds does it take Mackenzie to do one lap?

Question

Jess is running around a circular track, one lap every 40 seconds. Mackenzie is also running at a constant speed around the same track, but in the opposite direction. They meet every 15 seconds. How many seconds does it take Mackenzie to do one lap?

Answer 1

d1 = (15s/40s) * 1Lap = 15/40=3/8 Lap =

Jess' distance.

d1 + d2 = i Lap.
3/8 + d2 = 1
d2=1 - 3/8 = 5/8 Lap in 15s.=Mackenzie'
distance.

T = 15s/(5/8)Lap = 15 * 8/5 = 24 s/Lap.
= Mackenzie' speed.

Answer 2

To solve this problem, we can set up a proportion between Jess's lap time and Mackenzie's lap time.

Let's assume Mackenzie's lap time is x seconds.

Since Jess completes one lap every 40 seconds, her speed can be represented as 1 lap / 40 seconds.

Mackenzie, on the other hand, meets Jess every 15 seconds, so her speed can be represented as 1 lap / 15 seconds.

Now, we can set up the proportion:

1 lap / 40 seconds = 1 lap / x seconds

To solve for x, we can cross-multiply:

x = (40 * 1) / 1
x = 40 seconds

Therefore, it takes Mackenzie 40 seconds to complete one lap.

Answer 3

To find out how many seconds it takes Mackenzie to do one lap, we can start by finding the time it takes for Jess and Mackenzie to meet when they both start from the same point on the track.

Given that Jess completes one lap every 40 seconds, her speed is 1 lap per 40 seconds, or 1/40 laps per second. Since Mackenzie is running in the opposite direction, her speed is subtracted from Jess's speed.

When they meet every 15 seconds, this means that together they cover 1 lap in 15 seconds. To find the combined speed, we can use the formula:

Speed = Distance / Time

Since they both cover 1 lap when they meet, the distance is 1 lap. Plugging in the values we know, we have:

1 lap / 15 seconds = (1/40 + Mackenzie's speed) laps per second

Now, let's solve for Mackenzie's speed:

1/15 = 1/40 + Mackenzie's speed

Subtracting 1/40 from both sides:

1/15 - 1/40 = Mackenzie's speed

The least common denominator for 15 and 40 is 120, so let's convert the fractions:

(8/120) - (3/120) = Mackenzie's speed

Now, subtract the fractions:

5/120 = Mackenzie's speed

Simplifying the fraction:

1/24 = Mackenzie's speed

This means that Mackenzie's speed is 1/24 laps per second. Since we want to find how many seconds it takes for her to do one lap, we can invert the fraction:

24/1 laps per second.

Therefore, it takes Mackenzie 24 seconds to complete one lap around the track.