need help please?

Question

58. Science and medicine. 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?

Answer 1

He catches her at 1:00 PM
Read the question, people!
-------------------------------------

John spends time t on the road.
Martina spends time (t+2) on the road, as she leaves 2 hours before John (read the question!), not 1 hour as two of the previous posters have said.

They meet at distance x = (speed1)(time1) = (speed2)(time2)

(24 mph)(t + 2) = (48)t
24t + 48 = 48t
48 = 24t

t = 2 hours - John's driving time

As the question states, John leaves 2 hours after Martina, so he LEAVES at 11:00 AM. He then drives for 2 hours, catching up with her at 1:00 PM

Since he didn't leave until 11:00 A, he can't catch her at 11:00A, as everyone else so far has said - all of you previous posters can now edit and correct your answers...
:-/

Answer 2

Draw graph with x (miles) on the vertical axis, and t (hours) on the horizontal axis. Draw a line from the origin increasing slightly to the right. This is the line describing Martina's trip. At t=0, x = 0 and the slope is 24 mi/hr so the equation is
x = 24 t

Now draw a much steeper line starting from t = 1, increasing to the right. This is the line describing John's trip. The slope is 48 mi/hr. The equation is
x = 48t + b
To find b, use the fact that x = 0 at t = 1
0 = 48(1) + b
b = -48
x = 48t - 48
Equating the two x's
24 t = 48 t - 48
-48 = 24 t
t = 2
Answer: 11:00 AM

Answer 3

LOL!!! the first 3 previous responders are all "top contributor" but they got the wrong answer.

let t be the time Maria left. 2 hours later, or t- 2, john began to leave

24t = 48(t-2)
24t = 48t - 96
-24t = -96
t = 4hrs

John catches martia at 1:00 Pm

Answer 4

let t be the time Martina left, one our later, t-1, is the time Johe left.

when John caught Martina, their distances will be the same
distance of Martina: x = 24t
distance of John : x = 48(t-1)

24t = 48(t-1)
24t = 48t - 48
-24t = -48
t = 2

John caught up with Martina at 11:00 am

Hope this helps


EDIT: Mamamia is right!! lol!!

Answer 5

24t+48 = 48t
48t-24t = 48
t(48-24)=48
t = 2 hrs so he catches up with her at 11 A.M.

Doug