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

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

-6 is the correct option from the above given options