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Answer :
Final answer:
To calculate the time for a plane to overtake a helicopter that left earlier, we find the helicopter's head start distance, determine the relative speed between them, and then calculate the time with the formula distance/speed. It takes 24 minutes for the plane to catch up.
Explanation:
The question involves calculating the time it takes for a plane flying at 330 mi/hr to overtake a helicopter that left 20 minutes earlier flying north at 180 mi/hr. We approach this problem by first determining the head start distance of the helicopter. Given that 20 minutes is 1/3 hour, the helicopter flies 1/3 hour × 180 mi/hr = 60 miles before the plane takes off.
Next, we calculate the relative speed between the plane and the helicopter, which is 330 mi/hr - 180 mi/hr = 150 mi/hr. This speed indicates how fast the distance between them is closing.
To find how long it takes the plane to cover the 60 miles gap at a speed of 150 mi/hr, we use the formula time = distance / speed. Therefore, it takes the plane 60 miles / 150 mi/hr = 0.4 hours, or 24 minutes, to overtake the helicopter.
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Answer:
Step-by-step explanation:
Let x represent the distance travelled by the helicopter and the plane.
Let t represent the time it takes the the helicopter to travel x miles
Speed of the helicopter is 180 miles per hour.
Distance travelled = speed × time
x = 180t
Twenty minutes later, a plane leaves the airport and follows the helicopter at 330mi/hr. Converting 20 minutes to hours, it becomes 20/60 minutes
Time taken for the plane to travel x miles is t - 20/60
x = 330(t - 20/60)
Before the plane overtakes the helicopter, they would have travelled equal distance. Therefore
330(t - 20/60) = 180t
330t - 110 = 180t
330t - 180t = 110
150t = 110
t = 110/150 = 0.73 hours
