Two persons 'A' and 'B' walk round a circle whose 0diameter is 1.4 km. A walks at a speed of 100 meters per minute while B walks at a speed of 110 meters per minute. If they both start at the same time, from the same point and walk in the same direction, at what interval of time would they both be at the same starting point again?
Answers
Answer:
Diameter of the circle =1.4cm
⇒ Circumference =2πr =2×
7
22
×
2
1.4
km=4.4km
A's speed =165m/min
∴ Time taken by A to travel 4.4 km (4400 m)=
165
4400
min=
3
80
min
B's speed = 110 m/ min
∴ Time taken by B's to travel 4.4 km (4400 m) =
110
4400
min=40min
Required interval of time = LCM of (
3
80
,40)
=
HCF(3,1)
LCM(80,40)
=
1
80
min=
60hrs
80
=1
3
1
hrs
pls brainlist
Step-by-step explanation:
Given :-
Two persons 'A' and 'B' walk round a circle whose diameter is 1.4 km. A walks at a speed of 100 meters per minute while B walks at a speed of 110 meters per minute.
To find :-
If they both start at the same time, from the same point and walk in the same direction, at what interval of time would they both be at the same starting point again?
Solution :-
Given that
Diameter of the circle (d) = 1.4 km
We know that
Circumference of a circle = 2πr units or
πd units
Where ,r = radius of the circle
and d = diameter of the circle
Now
Circumference of the circle (C)
=>(22/7)×1.4km
=> (22×1.4)/7
=> 22×0.2
=> 4.4 km
Circumference of the given circle =
4.4 km
We know that
1 km = 1000 m
=> 4.4 km = 4.4×1000 = 4400 m
Now,
Given that
Speed of the person A = 100 meters /minutes
We know that
Distance = Speed × Time
=> Time = Distance / Speed
Time taken to A for walking the distance of 4400 m
=> T = 4400/100 minutes
=> T = 44 minutes
Time taken for walking the distance by A = 44 minutes
Speed of the person B = 110 meters/minutes
Time taken for covering the distance
=>4400/110
=> 440/11
=> 40 minutes
Time taken for walking the distance by B = 40 minutes
We have ,
Time taken by A= 44 minutes
Time taken by B = 40 minutes
If they both start at the same time, from the same point and walk in the same direction, an interval of time they will both be at the same starting point again is the LCM of times taken by both of them
LCM of 44 and 40
44 = 2×2×11
40 = 2×2×2×5
LCM = 2×2×2×5×11 = 440 minutes
We know that
60 minutes = 1 hour
1 minute = 1/60 hours
440 minutes = 440/60 hours
=>44/6 hours
=>22/3 hours
=> 7 1/3 hours
Answer:-
Required Interval of time they will both at the same starting point again for the given problem is 7 1/3 hours
Used formulae:-
- Circumference of a circle = 2πr or πd units
- Where ,r = radius and d = diameter
- Distance = Speed × Time
- 1 km = 1000 m
- 1 hour = 60 minutes