Respuesta :
Answer:
they meet after = 18 minutes 36 seconds
they meet at = 01:48:36 pm
Step-by-step explanation:
given data
area = 840 acres
wide = 1/2 mile
A mile = 5280 feet
1 acre = 43,560 square feet
One walks = 10 mph
other walks = 10 mph
solution
first we get here area of the park
Area = 840 acres = 840× 43560 sq ft
and
Width of the park will be
B = 1/2 mile = (1/2)×5280 2640 ft
so length will be here
length ( L ) = Area ÷ width ...............1
L = 840 × 43560 ÷ 2640
L = 13860 ft
and
perimeter = 2(L+B) .................2
perimeter =2(13860+2640)
perimeter = 33000 ft
so
when they start after they meet again when they together cover the perimeter of park
so
1st person speed = 10 mph = 52800 ft/hour
and
2ns person speed = 10 mph = 52800 ft per hour
so total distance cover both in 1 hour = 52800+52800
total distance cover = 105600 ft
so they meet after = 33000 ÷ 105600
they meet after = 0.31 hour = 00:18:36
they meet after = 18 minutes 36 seconds
and
TIME at which they will meet
they meet at = 01:30:00 pm + 00:18:36
they meet at = 01:48:36 pm
The time it takes one person to walk round the park is half the time it will
take two people walking in opposite to cover the perimeter of the park.
The Correct Response;
- The time it takes until they meet again is 18.75 minutes.
Given parameter;
Shape of Central park = A rectangle
Area central park = 840 acres
1 Acre = 43,560 ft.²
Width of Central park = 1/2 a mile
Starting location of the two people = South-west corner
Time at which the two people starts walking = 1:30 p.m.
Direction in which the two people walk = Opposite direction
The speed of the two people = 10 mph each
Required:
The duration it takes until they meet again.
Solution:
1 mile = 5,280 feet
Therefore;
1/2 mile = 5,280 feet ÷ 2 = 2,640 feet
The length of Central park = 840 × 43,560 ft.² ÷ 2,640 ft. = 13,860 ft.
Perimeter of the park = 2 × (13,860 ft. + 2,640 ft.) = 33,000 ft. = 6.25 mile
Given that the people walk in opposite direction, their combined speed, or
the relative speed of one taking the other as remaining stationary is
therefore;
Combined Speed = 10 mph + 10 mph = 20 mph = 20
[tex]\displaystyle Time = \mathbf{\frac{Distance}{Speed}}[/tex]
The time until they meet again is therefore;
[tex]Time = \mathbf{ \dfrac{Perimeter \ of \ Central \ park}{Combined \ speed}}[/tex]
Which gives;
[tex]Duration \ it \ takes = \dfrac{6.25 \ mile}{20 \ mph} = \mathbf{0.3125 \ hour}[/tex]
The duration it takes for them to meet again = 0.3125 hour
Converting to minutes, we have;
- Duration until they meet again = 60 × 0.3125 minutes = 18.75 minutes
Learn more about relative speed here:
https://brainly.com/question/13827814
https://brainly.com/question/948670
