A jet plane traveling at 500 mph overtakes a propeller plane traveling at 200 mph that had a 2-hour head start. How far from the starting point are the plains?
the went the same distance
and the difference in their times is 2
let me see your setup of the equation
To find the distance from the starting point, we need to determine the time it takes for the jet plane to overtake the propeller plane.
Let's calculate the time it takes for the jet plane to catch up to the propeller plane:
Distance traveled by the propeller plane = Speed × Time
Since the propeller plane had a head start of 2 hours, the time it took for the propeller plane to reach the starting point is 2 hours.
Distance traveled by the jet plane = Speed × Time
Since we don't know the exact time when the jet plane overtakes the propeller plane, we can assume the time taken by both planes is the same.
Therefore, Distance traveled by the jet plane = Distance traveled by the propeller plane
So, we can establish the equation:
500 mph × Time = 200 mph × (Time + 2 hours)
Let's solve this equation to find the value of Time:
500mph × Time = 200mph × Time + 400mph
500mph × Time - 200mph × Time = 400mph
300mph × Time = 400mph
Time = 400mph / 300mph
Time = 4/3 hours
Now, we know it takes 4/3 hours for the jet plane to catch up to the propeller plane. To find the distance from the starting point:
Distance = Speed × Time
Distance = 500 mph × 4/3 hours
Distance ≈ 666.67 miles
So, the planes are approximately 666.67 miles from the starting point.