Question

A certain space shuttle travels at a speed of 3.6 x 104 miles per hour. How

many hours would it take this space shuttle to travel 7.2 * 108 miles?
А) 5.0 - 10-5
B) 25.9 -10°
с) 2.0102
D) 2.0 104
E) 25.9 - 1012

Answer 1

The time it takes for the space shuttle to cover
`\(7.2 * 10^8\)` miles at a speed of
`\(3.6 * 10^4\)` miles per hour is
`\(2.0 * 10^4\)` hours, simplified to
`\(25.9 * 10^2\)`, or 2590 hours, option B 25.9 -10°

Step-by-step explanation:

The time it takes for the space shuttle to travel a certain distance is determined by the formula:
`\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]`

In this case, the distance is
`\(7.2 * 10^8\)` miles and the speed is
`\(3.6 * 10^4\)` miles per hour. Plugging these values into the formula, we get:

`\[ \text{Time} = (7.2 * 10^8)/(3.6 * 10^4) \]`

Simplifying this expression, we can cancel out a factor of 10^4 from the numerator and denominator, resulting in:

`\[ \text{Time} = (7.2 * 10^(8-4))/(3.6) \]`

Further simplifying, we find:

`\[ \text{Time} = (7.2 * 10^4)/(3.6) \]`

Now, dividing 7.2 by 3.6 gives us 2.0, and we are left with:

`\[ \text{Time} = 2.0 * 10^4 \]`

Converting this into scientific notation, we get
`\(2.0 * 10^4\)`, which is equivalent to 20,000 hours.

Therefore, the correct answer is option B:
`\(25.9 * 10^2\)`. This can be further expressed as
`\(25.9 * 100\)`, which equals 2590 hours. Thus, the space shuttle would take 2590 hours to travel
`\(7.2 * 10^8\)` miles at a speed of
`\(3.6 * 10^4\)` miles per hour.