Dori and Malory are tracking their steps taken as a health goal. Dori leaves her house at 12:00 p.m. and walks at 50 steps per minute. Malory leaves her house at 12:20 p.m. and walks at 90 steps per minute.
At what time will Malory's steps catch up to Dori's steps?
50steps/min * 20min = 1000 Step head-start for Dori.
90 * T = 50 * T + 1000.
90T = 50T + 1000
T = 25 min. to catch up.
To determine the time when Malory's steps will catch up to Dori's steps, we need to find the time it takes for Malory to walk the same number of steps as Dori.
Let's calculate the steps Dori takes first.
Dori walks at 50 steps per minute, and Malory starts 20 minutes later. So Dori has a head start of 50 steps/minute * 20 minutes = 1000 steps.
Let's denote the time it takes for Malory to catch up to Dori as t minutes.
Malory walks at 90 steps per minute, so her steps taken in t minutes would be 90 steps/minute * t minutes = 90t steps.
Since we want Malory's steps to be equal to Dori's steps when they catch up, we can set up the equation:
1000 steps + 90t steps = t minutes * 90 steps per minute
Simplifying the equation, we have:
1000 steps = t minutes * 90 steps per minute - 90t steps
1000 steps = 90t minutes - 90t steps
1000 steps = 90t minutes - 90t steps
1000 steps = 90t (minutes - steps)
1000 steps = 90t
Solving for t, we have:
t = 1000 steps / 90 steps per minute
t = 11.11 minutes
So Malory's steps will catch up to Dori's steps approximately 11.11 minutes after Malory starts walking.
Since Malory starts walking at 12:20 p.m., we add 11.11 minutes to this time to find the time Malory's steps catch up to Dori's:
12:20 p.m. + 11.11 minutes = 12:31:06 p.m.
Therefore, Malory's steps will catch up to Dori's steps at approximately 12:31:06 p.m.
To find the time when Malory's steps catch up to Dori's steps, we need to calculate the number of steps each person takes.
Dori starts walking at 12:00 p.m. and walks at a rate of 50 steps per minute. So, by the time Malory starts at 12:20 p.m., Dori would have already been walking for 20 minutes.
The number of steps Dori would have taken in these 20 minutes can be calculated as:
Steps taken by Dori = 50 steps/minute * 20 minutes = 1000 steps
So, when Malory starts walking at 12:20 p.m., she needs to catch up with the 1000 steps that Dori has already taken.
Now, let's calculate the rate at which Malory is walking:
Malory walks at a rate of 90 steps per minute.
To find the time it takes for Malory to catch up with Dori's 1000 steps, we can use the formula:
Time = Steps / Rate
Time = 1000 steps / 90 steps/minute = 11.11 minutes
Since Malory starts walking at 12:20 p.m., it will take her approximately 11.11 minutes to catch up with Dori's steps. Adding this time to 12:20 p.m. gives us the time when Malory catches up to Dori's steps:
12:20 p.m. + 11.11 minutes = approximately 12:31 p.m.
Therefore, Malory's steps will catch up to Dori's steps at approximately 12:31 p.m.