A planet has a circular orbit around a star. It is a distance of 59,000,000 km from the centre of the star. It orbits at an average speed of 41,000 km/h. How many Earth days does it take the planet to orbit the star? Give your answer to 2 sf.

380 days

Step-by-step explanation:

Problem in post:

The radius of the orbit of the planet is 59,000,000 km.

The orbit is circular, so the length of the orbit is the circumference of a circle with radius 59,000,000 km.

distance = circumference of orbit = 2(pi)r = 2 * 3.14159 * 59,000,000 km = 370,707,933 km

speed = 41,000 km/h

speed = distance/time

time * speed = distance

time = distance/speed

time = (370,707,933 km)/(41,000 km/h) = 9,042 hours

Now we convert hours into earth days.

1 earth day = 24 hours

9,042 hours * (1 day)/(24 hours) = 376.73 days

380 days

Problem in comments:

Nina and Jo both ran an 8 km race.

Nina took 45 minutes to run the whole race.

Jo started the race 4 minutes later than Nina but caught up when they had both travelled 5 km.

If Nina and Jo both ran at constant speeds, what is Jo's speed to 2 dp?

Solution:

They met at 5 km. Let's find out how long it took Nina to run 5 km.

We can use a proportion.

(8 km)/(45 min) = (5 km)/(x)

x * 8 km = 45 min * 5 km

x = [(45 * 5)/8] min

x = 28.125 min

They met after Nina was running for 28.125 minutes.

Jo started 4 minutes after Nina, so Jo ran for 4 minutes less than Nina. Jo ran 5 km in 24.125 minutes.

speed = distance/time

speed = (5 km)/(24.125 min) * (60 min)/(1 hr)

speed = 12.43523 km/h

Jo's speed is 12.44 km/h

the answer is 0.3175 hope that you ^w^

also you might actually want to put this picture up if you want people to solve it luckily i remember this question

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.