A plane leaves an airport and flies south at 120 mph. Later, a second plane leaves the same airport and flies south at 300 mph. If the second plane overtakes the first one in
5
1
2
hours, how much of a head start did the first plane have?
Are there 3 questions here ??
I will consider the last one, so it would read:
"A plane leaves an airport and flies south at 120 mph. Later, a second plane leaves the same airport and flies south at 300 mph. If the second plane overtakes the first one in 2 hours, how much of a head start did the first plane have?"
in effect the second plane is gaining on the first plane at 180 mph, so in 2 hours it would have to make up 360 miles, which would be the head-start.
check: distance covered by slower plane = 360 + 120(2) = 600
distance covered by faster plane = 300(2) = 600
My answer is correct.
do the other two problems in the same way
300*5 = 120*5 + 120x
Solve for x. Do the same for 1 and 2.
To determine the head start of the first plane, we need to find the distance it traveled before being overtaken by the second plane.
Let's assume that the distance traveled by the second plane to overtake the first plane is "d" miles.
The speed of the first plane is 120 mph, and it was traveling for 5.5 hours (5 1/2 hours) before being overtaken. Therefore, the distance traveled by the first plane can be calculated using the formula distance = speed × time:
Distance = 120 mph × 5.5 hours = 660 miles
Since the second plane overtakes the first plane after traveling "d" miles, we can set up an equation:
d = 300 mph × 5.5 hours
d = 1650 miles
Now, we know that the second plane traveled 1650 miles to overtake the first plane. Therefore, the head start of the first plane is the difference in distance traveled by the first plane and the second plane:
Head start = Distance traveled by the first plane - Distance traveled by the second plane
Head start = 660 miles - 1650 miles
Head start = -990 miles
Since the head start is negative, it means that the first plane was behind the second plane at the time of departure. Therefore, the first plane had a head start of 990 miles behind the second plane.