How do you solve these types of problems.?
Martina leaves home at 9.A.M., bicycling at a rate of 24mi/h. Two hours later, John leaves, driving at the rate of 48mi/h. At what time will John catch up with Martina?
The basic formula is
distance= speed*time
However, remember that if some time is later than t, then that time is t-a, where a is the time later.
The distance they go is the same.
distance=24*time
distance=48(time-2)
solve for time. Add 9 am to get the clock (24 hour time).
We will be happy to critique your work.
what does all this mean?
leah--Please post it if you have a question.
Martina leaves home at 9 A.M., bicycling at a rate of
24 mi/h. Two hours later, John leaves, driving at the rate of 48 mi/h. At what time
will John catch up with Martina?
To solve this problem, we need to understand that John is starting two hours later than Martina and we want to find the time at which they meet.
Let's break down the problem step by step:
1. Martina's distance: Martina starts at 9 A.M. and travels at a rate of 24 mi/h. Since speed is equal to distance divided by time, we can use the formula distance = speed * time to find Martina's distance traveled. Let's call Martina's time t.
Distance = Speed * Time
Martina's Distance = 24 * t
2. John's distance: John starts two hours later than Martina, so we need to take into account the time difference. We can represent John's time as t - 2, where t is the time at which they meet.
Distance = Speed * Time
John's Distance = 48 * (t - 2)
3. Since they meet at the same point, Martina's distance is equal to John's distance. We can set up an equation to represent this:
Martina's Distance = John's Distance
24 * t = 48 * (t - 2)
4. Now, we need to solve this equation for t to find the time at which they meet. Let's simplify the equation:
24t = 48t - 96
24t - 48t = -96
-24t = -96
t = -96 / -24
t = 4
The value of t represents the number of hours after 9 A.M., so we can add it to the starting time of 9 A.M. to find the time at which John catches up with Martina.
9 A.M. + 4 hours = 1 P.M.
Therefore, John will catch up with Martina at 1 P.M.