Question

Two rockets are to be launched at the same time from NASA headquarters in Florida, and are to meet at a space station many miles from Earth. The first rocket is to travel at 20,000 miles per hour and the second rocket will travel at 14,000 miles per hour. If the first rocket is scheduled to reach the space station 0.9 of an hour before the second rocket, how far is the space station from NASA headquarters?

A) 9,000 miles
B) 10,000 miles
C) 11,000 miles
D) 12,000 miles

Answer 1

The calculated distance to the space station is 42,000 miles based on the given speeds and time difference of arrival for the two rockets. However, this result doesn't match any of the provided multiple-choice options, indicating a possible error in the question or options.

Step-by-step explanation:

To solve this problem, we will use the concept of relative speed and the relationship between speed, distance, and time. Let's denote the distance to the space station as D. We know that the first rocket travels at 20,000 miles per hour and arrives 0.9 hours earlier than the second rocket, which travels at 14,000 miles per hour.

The time it takes for the first rocket to reach the space station is t, and for the second rocket, it would be t + 0.9 hours. Using the formula distance = speed × time, we can set up the following equations:

For the first rocket: D = 20,000 × t

For the second rocket: D = 14,000 × (t + 0.9)

Since both rockets reach the same distance D, we can set the equations equal to each other and solve for t:

20,000 × t = 14,000 × (t + 0.9)

20,000t = 14,000t + 12,600

6,000t = 12,600

t = 2.1 hours

Using the value of t in the first equation, we can find the distance D:

D = 20,000 × 2.1

D = 42,000 miles

None of the options given (A) 9,000 miles, (B) 10,000 miles, (C) 11,000 miles, (D) 12,000 miles match the calculated distance of 42,000 miles. There might be a mistake in the question or the provided options.