Please can you help

[granny grump]

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?

[bibblebub]

q4 Assuming it travels the same distance going up as coming back down, consider the time taken:

For a distance X miles, time going up = X/3000, time coming down = X/1000

therefore total time = X/3000 + X/1000 = 4X/3000
total journey = 2X miles (going up + coming down)

thus average speed (disatnce / time) = 2X / (4X/3000) = 6000X/4X = 1500 mph.

[bibblebub]

perhaps should add that since speed = distance / time
re-arranging that gives time = distance / speed

[granny grump]

Thank you for your help bibblebub - I don't know if it came across in my post - but I am really cross with him

[bibblebub]

In that case I'd better apologise for not being particularly lucid at this time of a Sunday morning.

q5 consider that how far they each will have travelled around their orbit until aligned again. Each day, Mercury travels 1/89 of its orbit (assume the are circular orbits to keep the sums simple) whereas the Earth will have moved by 1/365.25 of it orbit. They will meet up when Mercury is done more than 1 orbit and so (if t is the number of days)

t/89 = 1+(t/365.25)

=> (t/89) - (t/365.25) = 1, and so calculate t

[bibblebub]

q7 too difficult to think clearly at this time of the day

[granny grump]

Thank you bibblebub - sorry to tax you so early