A rocket blasts off from Earth heading for Mars, getting faster as it travels. In fact, the rocket’s speed doubles every week that it’s in space. If the rocket lands on Mars in week 12, in which week was it halfway there?
Answers
Given : A rocket blasts off from Earth heading for Mars, getting faster as it travels.
the rocket’s speed doubles every week that it’s in space.
the rocket lands on Mars in week 12,
To Find : in which week was it halfway there
Solution:
Assuming it landed at the end of 12 week.
Let say Initial Speed = x unit / wk
Distance = speed x Time
Distance covered in 1st week = x unit
rocket’s speed doubles every week
so speed in 2nd week = 2x unit / wk
Hence Distance covered in 2nd week = 2x unit
So Distance covered in 12 weeks
= x + 2x + 4x + ___________ 2¹⁰x + 2¹¹x
a = x r = 2 n= 12
Total Distance covered = x(2¹² - 1) / ( 2 - 1)
= x(2¹² - 1)
= 4095x
Mid way = 4095x/2 = 2047.5x
Distance covered in last week = 2¹¹x = 2048x
Distance covered in 11 weeks = 2047x
Hence 2047x to 2047.5x will be covered in week 12
Hence in Week 12 ( almost at the beginning) it halfway
Assuming it landed in between of 12 week.
Then in Week 11 it halfway
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