Question

Maggie lives 1250 meters from school. Ming lives 800 meters from school. both girls leave school at the same time. Maggie walks at an average speed of 70 meters per minute, while Ming walks at an average speed of 40 meters per minute. Maggi's route takes her past Ming's house.
Answet part A-C by writing and solving the equations and inequalities.
a) When, if ever, will maggie catch up with ming?
b) How long will maggie remain behind Ming?
c) At what times is the distance between the two girls less than 20 meters?

Answer This People :\

Answer 1

a) Define t as time in minutes
we have 70t = 40t + 450
Solve the equation we have t = 15. Thus 15 minutes

b) I don't understand. How long in time or in distance? If in time, maggie remains behind Ming until she catches up with Ming.

c) we have the equation
70t+20=40t+450
30t=430
t= 14 1/3

Answer 2

But number a ,probably would be in this way as follow?

70 m takes= 1 min
1 m takes = 1 / 70
800 m takes= 1*800/700 = 11 mins
No?

Answer 3

For part A, anyhuyalex has the correct equation, which is the tough part of doing this problem. Here's how I think of it: Ming has a head start of 450 m over Maggie. They start at the same time, and if they meet, it must be each walked the same amount of time up to that point. The difference is that Maggie had to walk further ( and of course) faster. So in time t Maggie walks 70 t meters. But we know this distance must be the extra distance from Maggie to Ming's house (450 m) plus the amount Ming walked, 40 t. So we get the equation
70 t = 40 t + 450
Solve for t to get 15 minutes. Now, we should check that Ming did not get to school already: in 15 minutes Ming walks 40*15= 600 m which is less than 800 m. Good! Maggie caught up to her 200 m from the school.

Part B, I assume means time, so Maggie was behind Ming for 15 minutes.

Part C, think relative velocity. Maggie is closing in on Ming at 30 m/min. So once they have met, Maggie moves away from Ming at 30 m/min. To get 20 m in front, use t= d/v or t= 20/30 or 2/3 of a minute. Call this time 15:40 (time is 15 mins, 40 seconds). Also, Maggie was behind Ming ( and closing in fast!) at 15 min - 2/3 minute or 14:20. So between 14:20 and 15:40 Maggie and Ming were within 20 meters of each other.