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

Answer: 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

Answer: Jo's speed is 12.44 km/h