Two planes flying opposite directions (north and south) pass each other 80 miles apart at the same altitude. The northbound plane is flying 200 mph (miles per hour) and the southbound plane is flying 150 mph. How far apart are the planes in 20 minutes? (Round your answer to one decimal place.)
This is what I did
Distance between these planes after 20 minutes or 1/3 hours.
In right angle triangle DEC,
DE = 80 miles
BE = (Speed × duration) = 200*1/3= 66.666667miles
Similarly, BC = 150*1/3=50 miles
By Pythagoras theorem,
DC² = EC² + DE²
= (EB + BC)² + DE²
= (66.67+ 50)² + (80)²
= 20011.8889
DC = √20011.8889 = 141.46 miles
What did I do wrong
Looks good to me.
Well, it seems like you've done the calculations correctly. However, you made a small mistake in your final answer. The correct distance between the planes after 20 minutes is approximately 141.5 miles (rounded to one decimal place), not 141.46 miles. So you were pretty close! Remember to round your final answer to the specified decimal place. Keep up the good work!
Your calculations are correct, but there is a mistake in the values you used for the speeds of the planes. The northbound plane is flying at 200 mph, so its distance covered in 20 minutes would be (200 * (20/60)) = 66.67 miles. Similarly, the southbound plane is flying at 150 mph, so its distance covered in 20 minutes would be (150 * (20/60)) = 50 miles.
Using these corrected values, the calculation would be as follows:
Distance between these planes after 20 minutes or 1/3 hours.
In right angle triangle DEC,
DE = 80 miles
BE = (Speed × duration) = 66.67 miles (corrected)
Similarly, BC = 50 miles (corrected)
By Pythagoras theorem,
DC² = EC² + DE²
= (EB + BC)² + DE²
= (66.67 + 50)² + 80²
= 20011.8889
DC = √20011.8889 = 141.46 miles
So, the corrected answer is that the planes are 141.46 miles apart after 20 minutes.
Your calculations appear to be correct. However, there might be a rounding error in the final answer.
After solving for DC², you correctly got 20011.8889. Taking the square root of this value would give you the distance DC:
√20011.8889 = 141.4598...
Rounding this to one decimal place would give you an answer of 141.5 miles, not 141.46. So, the final answer to the question "How far apart are the planes in 20 minutes?" would be 141.5 miles.