Answer:
Question 1: They will be 1400 miles apart after 4/3 hours (1 hr and 20 min)
Question 2: The time will be 9:20 AM.
Question 3: Plane 1 has traveled 800 miles, Plane 2 has traveled 600 miles
Step-by-step explanation:
* Lets explain how to solve the problem
- Two planes leave the same point at 8 AM
- Plane 1 head east at 600 mph
- Plane 2 head west at 450 mph
# Question 1:
- After t hours the distance between them will be 1400 miles
∵ The speed of plane 1 is 600 mph
∴ The distance it has moved in t hours = 600 × t = 600t
∵ The speed of plane 2 is 450 mph
∴ The distance it has moved in t hours = 450 × t = 450t
∵ Plane 1 head east and and plane 2 head west
- East and west are on the same line but in opposite direction
∵ The distance between them after t hours is 1400 miles
∴ Distance of plane 1 + distance of plane 2 = 1400
∴ 600t + 450t = 1400
∴ 1050t = 1400 ⇒ divide both sides by 1050
∴ t = 4/3
∴ They will be 1400 miles apart after 4/3 hours (1 hr and 20 min)
# Question 2:
∵ The two planes leave at 8 AM.
∵ They move for 1 hour and 20 minutes
∴ The time will be 9:20 AM.
# Question 3:
∵ The speed of plane 1 is 600 mph
∵ It has traveled for 4/3 hours
∴ Its distance = 600 × 4/3 = 800 miles
* Plane 1 has traveled 800 miles
∵ The speed of plane 2 is 450 mph
∵ It has traveled for 4/3 hours
∴ Its distance = 450 × 4/3 = 600 miles
* Plane 2 has traveled 600 miles
(1). Planes will be 1400 miles apart after [tex]1\frac{1}{3}[/tex] hours.
(2). Both the planes will be 1400 miles apart at 9:20 A.M.
(3). Plane 1 and plane 2 will travel 800 miles and 600 miles respectively.
Speed of an object is given by,
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]
(1). Given in the question,
Let both the planes travel for 't' hours,
Distance traveled by 1st plane = Speed × Time
= 600 × t
Distance traveled by 2nd plane = 450 × t
Distance between these planes = 1400 miles
Therefore, equation for the total distance traveled by them will be,
600t + 450t = 1400
Simplify the equation for the value of 't'
1050t = 1400
t = [tex]1\frac{1}{3}[/tex] hours
Therefore, both the planes will be 1400 miles apart after [tex]1\frac{1}{3}[/tex] hours.
(2). Both the planes left at 8 A.M.
After traveling for [tex]1\frac{1}{3}[/tex] hours, time will be → 8 + [tex](1+\frac{1}{3}\times 60)[/tex] = 9.20 A.M.
Therefore, at 9.20 AM both the plane will be 1400 miles apart.
(3). Distance traveled = Speed × Time
Distance traveled by plane 1 = [tex]600\times \frac{4}{3}[/tex]
= 800 miles
Distance traveled by plane 2 = [tex]450\times \frac{4}{3}[/tex]
= 600 miles
Therefore, distances traveled by the planes 1 and plane 2 will be
800 miles and 600 miles respectively.
Learn more about the speed, distance and time here,
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