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I am helping my grandson with his home work - the little monkey rang last night after a week with us and us asking if he had any homework to say that he had 'forgotten' to do his homework. Monkey - but typical!!! he thinks his nan knows everything - but she doesn't. I don't want him to get into trouble but neither do I want just to give him the answers.
Please can you show me how to work these out so that he can then do it himself. If you do provide the answers I can then check his work
Question 4 - Trouble at Hubble
In 1990, the Hubble Space Telescope was launched. Twenty-one years on, it was in need of repair, and a rocket was sent into space to repair it. The rocket made good progress on the way up to the telescope, travelling at an average speed pf 3,000 mph. Whilst at the telescope, the rocket developed a fault and the rocket's speed on the return jurney was reduced to 1,000 mph. What was the overall average speed of the rocket?
Question 5 - Line Dancing
Mercury orbits the sun in 89 days, Earth orbits in 365.25 days. If, at midnight on 21st December 2010, the panets are in alignment on the same side of the sun, on which dates will Mercury pass between the Earth and the Sun during 2011?
Question 7 - Space Men
Toy space men of different shapes are each formed from five 1cm cubes, with adjacent cubes firmly welded together face to face. To qualify for space flight, each space man has to be able to fit into a 3cm x 3xm x 3cm escape pod. How many such space men are there, each distinct from the other?
Please can you show me how to work these out so that he can then do it himself. If you do provide the answers I can then check his work
Question 4 - Trouble at Hubble
In 1990, the Hubble Space Telescope was launched. Twenty-one years on, it was in need of repair, and a rocket was sent into space to repair it. The rocket made good progress on the way up to the telescope, travelling at an average speed pf 3,000 mph. Whilst at the telescope, the rocket developed a fault and the rocket's speed on the return jurney was reduced to 1,000 mph. What was the overall average speed of the rocket?
Question 5 - Line Dancing
Mercury orbits the sun in 89 days, Earth orbits in 365.25 days. If, at midnight on 21st December 2010, the panets are in alignment on the same side of the sun, on which dates will Mercury pass between the Earth and the Sun during 2011?
Question 7 - Space Men
Toy space men of different shapes are each formed from five 1cm cubes, with adjacent cubes firmly welded together face to face. To qualify for space flight, each space man has to be able to fit into a 3cm x 3xm x 3cm escape pod. How many such space men are there, each distinct from the other?
Answers
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You are wrong, Johne1892. You can only take a mean average of speeds if the time is the same (not the distance).
I'll try not to use algebra although algebra can be useful here.
Speed = distance divided by time.
Suppose the distance each way is 30000 miles. The time taken in hours for the upward trip at 3000 mph is 10 hours. The time taken for the down trip at 1000 mph is 30 hours.
The total distance is 60000. The total time is 40 hours. The average speed is therefore 60000/40= 1500 mph.
Change the distances and you will always get the same result. For example if distance = 3000 miles. The upward time is 1 hour and the downward time is 3 hours. So the total time is 4 hours. Average speed = 6000/ 4= 1500 mph
I'll try not to use algebra although algebra can be useful here.
Speed = distance divided by time.
Suppose the distance each way is 30000 miles. The time taken in hours for the upward trip at 3000 mph is 10 hours. The time taken for the down trip at 1000 mph is 30 hours.
The total distance is 60000. The total time is 40 hours. The average speed is therefore 60000/40= 1500 mph.
Change the distances and you will always get the same result. For example if distance = 3000 miles. The upward time is 1 hour and the downward time is 3 hours. So the total time is 4 hours. Average speed = 6000/ 4= 1500 mph
A good example is the problem of a car that drives one mile up a hill at 30 mph and then drives one mile down the other side. What speed must he drive down at in order to make the average speed for the journey 60 mph.
The most common answer is 90 mph (since the average of 30 and 90 is 60) but in fact the answer is that it is impossible to achieve an overall average of 60 mph.
This is because the 1 mile journey up the hill at 30mph takes 2 minutes. To give an average of 60mph for the whole 2 mile journey the 2 miles would have to be completed in 2 minutes. But if it takes 2 mins to get up the hill the driver would have to get down the hill in zero seconds to achieve the target- and that's impossible.
The most common answer is 90 mph (since the average of 30 and 90 is 60) but in fact the answer is that it is impossible to achieve an overall average of 60 mph.
This is because the 1 mile journey up the hill at 30mph takes 2 minutes. To give an average of 60mph for the whole 2 mile journey the 2 miles would have to be completed in 2 minutes. But if it takes 2 mins to get up the hill the driver would have to get down the hill in zero seconds to achieve the target- and that's impossible.
Johne1892- what, after you've had a couple of pints or I've had a couple? I fall asleep after 2 pints these days (or is that what you meant!)
Notafish- if the car drove up at 20 mph the 1 mile journey up would take 3 minutes. To get an average speed of 60mph for the whole 2 mile journey you'd have to do the whole trip in 2 minutes, but that's impossible as it's already taken 3 minutes to get up.
If you go up at 40 mph then that would take 1.5 minutes. To give an overall time of 2 minutes you need to come down (1 mile) in half a minute which would require a speed of 120 mph.
Notafish- if the car drove up at 20 mph the 1 mile journey up would take 3 minutes. To get an average speed of 60mph for the whole 2 mile journey you'd have to do the whole trip in 2 minutes, but that's impossible as it's already taken 3 minutes to get up.
If you go up at 40 mph then that would take 1.5 minutes. To give an overall time of 2 minutes you need to come down (1 mile) in half a minute which would require a speed of 120 mph.
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