The speed of a journey is inversely proportional to the time the journey takes. Martin travels from home at a consent speed of 80km/h to get to work.
The journey takes him 2 1/2 hours.
He spends a few hours at work and then travels at an average speed of 90km/h to return home.
How long does this journey take?
Write your answer in hours and minutes to the nearest minute.
How do you work out this maths question?
2016-02-25 5:36 pm
回答 (2)
2016-02-25 5:48 pm
✔ 最佳答案
s : the speed of the journey in km/ht : time taken for the journey in h
s ∝ 1/t
Thus, s = k/t
where k is a non-zero constant.
When s = 80, t = 2.5 :
80 = k/2.5
k = 200
Then, s = 200/t
When s = 90 :
90 = 200/t
t = 200/90
Time taken at an average speed of 90 km/h
= 200/90 h
= 20/9 h
= 2 h [(2/9) × 60] min
= 2 h 13 min
2016-02-25 5:46 pm
Martin travels 9/8 times as fast home from work than he did to work.
Martin's time will be 9/8 times smaller.
2.5 hours * 8/9 = 2 hrs 13 min
Mathematically:
From home to work, distance = (v1)(t1) = 80(t1)
The other way, distance = (v2)(t2) = 90(t2)
80(t1) = 90(t2)
t2 = t1 * 90/80 = (9/8)(2.5 h)
Martin's time will be 9/8 times smaller.
2.5 hours * 8/9 = 2 hrs 13 min
Mathematically:
From home to work, distance = (v1)(t1) = 80(t1)
The other way, distance = (v2)(t2) = 90(t2)
80(t1) = 90(t2)
t2 = t1 * 90/80 = (9/8)(2.5 h)
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