Math help!!!!!!!!!!!!!!!!!!!!!!!!!!!!?

Question

A woman on foot leaves a restaurant heading west at noon. Three hours later, a man on a bicycle leaves the restaurant pedaling west at a rate of 12 miles per hour. At six o'clock that evening, a woman on a scooter leaves the restaurant driving west at a speed of 39 miles per hour. If the first woman was walking at a rate of 3 miles per hour, calculate the distances below.

There are three questions that need to be answered:

1: How far from the restaurant will the woman on foot be when the man on the bicycle reaches her?

2: How long will it take for the woman on the scooter to reach the woman on foot?

3. How far from the restaurant will the man on the bicycle be when the woman on the scooter reaches him?

Please answer!

im really stuck!! thx!

Answer 1

You can figure out how much of a head start the earlier departing person has, then how much per hour the later departing one gains, and go from there. For example, the woman on foot has a 3X3 = 9 mile head start on the bicyclist but he gains 12 - 3 = 9 miles an hour so he'll catch her in an hour.

Answer 2

Part 1:
Let the time be measured as 't'.
The distance traveled when the woman meets the cyclist will be the same (d=d). The time for the cyclist, however, will be three hours lass than the time for the woman.
Distance = Rate * Time
For the woman, d = 3 * t.
For the cyclist, d = 12 * (t - 3).
The distance is equal, so:
3t = 12(t-3),
3t = 12t - 36,
36 = 9t,
t = 4.
That's twelve miles.

Part 2:
Similar to part 1:
d = 3t,
d = 39(t - 6);
so
3t = 39(t - 6),
3t = 39t - 234,
234 = 36t,
t = 6.5 (hours), that's 19.5 miles away when they meet!

Part 3:
The woman on foot no longer needs considered- the offset of the man-on-bicycle and woman-on-scooter is three hours:
d = 12t,
d = 39(t - 3); so,
12t = 39(t - 3),
12t = 39t - 117,
117 = 27t,
so the time for the man-on-bicycle is 4.333 hours (the woman-on-scooter takes 1.333 hours).

Either way, the distance is 52 miles.

Feel free to email me for further clarifications.

Answer 3

1.
d = 3t =12(t - 3)
9t = 36
t = 4
d = 12 mi

2. same method
d = 3t =39(t - 6)
13t = 13*6
t = 6
d = 18 mi

3.
d = 12t =39(t - 3)
4t = 13t - 39
9t = 39
t = 13/3
d = 52 mi

Answer 4

1) x represent the woman leaves
3hr later, that means x-3, the man leaves

when the man catches the woman, the distances are equal.
3x= 12(x-3)
3x= 12x-36
-9x=-36
x= 4

x=vt
x=3(4)
x= 12miles
the woman walks 12miles when the man catches her.
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2) (x-6) is the time the scooter leaves
3x= 39(x-6)
3x= 39x-234
-36x=-234
x= 6.5hr

x=vt
x= 3(6.5)
x= 19.5mile

the woman walks 19.5 miles when the scooter reaches her.
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Answer 5

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