The distance from Earth to Mercury is 9.21 x 10^7 kilometers How long would it take a rocket, traveling at 5.72 x 10^4 kilometers per hour to travel from Earth to Mercury? Round your answer to the nearest whole number of hours

Answer 1

To calculate the time it would take the rocket to travel from Earth to Mercury, we can use the formula:

$$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$$

Given:

• Distance = $9.21\times {10}^7$ kilometers
• Speed = $5.72\times {10}^4$ kilometers per hour

Now, substituting the values into the formula:

$$\text{Time}=\frac{9.21\times {10}^7\text{ km}}{5.72\times {10}^4\text{ km/h}}$$

Calculating the division:

$$\text{Time}=\frac{9.21}{5.72}\times \frac{{10}^7}{{10}^4}$$

$$\text{Time}=\frac{9.21}{5.72}\times {10}^{7-4}$$

$$\text{Time}\approx 1.6077\times {10}^3\text{ hours}$$

Now, ${10}^3$ is 1000, so:

$$\text{Time}\approx 1.6077\times 1000=1607.7\text{ hours}$$

Rounding to the nearest whole number:

$$\text{Time}\approx 1608\text{ hours}$$

Thus, it would take approximately 1608 hours for the rocket to travel from Earth to Mercury.

Answer 2

A water park has pools, slides, and rides that, in total, make use of 9.1 x 10^7 gallons of water They plan to add a ride that would make use of an additional 280,000 gallons of water. Use scientific notation to express the total gallons of water made use of in the park after the new ride is installed

Answer 3

To express the total gallons of water after adding the new ride in scientific notation, we start with the initial amount of water and add the additional amount.

Given:

• Initial water usage: $9.1\times {10}^7$ gallons
• Additional water usage: 280,000 gallons

First, let's convert 280,000 gallons into scientific notation:

$$280,000=2.8\times {10}^5$$

Now we will add this to the initial water usage. To add the two numbers in scientific notation, they need to have the same exponent. Since the larger exponent is ${10}^7$, we will convert $2.8\times {10}^5$ to the same exponent:

$$2.8\times {10}^5=0.028\times {10}^7$$

Now we can add the two quantities:

$$9.1\times {10}^7+0.028\times {10}^7=(9.1+0.028)\times {10}^7$$

Calculating the sum:

$$9.1+0.028=9.128$$

Now we express this in scientific notation:

$$9.128\times {10}^7$$

Thus, the total gallons of water made use of in the park after the new ride is installed is:

$$\boxed{{\displaystyle 9.128\times {10}^7}}\text{ gallons}$$