Question 24 - Problems - Chapter 2¶

Problem:¶

You make a 100-km trip in an automobile, traveling the first 50 km at 60 km/h and the second 50 km at 80 km/h.

Question:¶

What is your average speed for this trip?

Explain why the average speed is not 70 km/h.

Solution:¶

The 100 km trip $s$ consists of two parts of 50 km each

Speed of the first half is $v_1 = 60$ km/h

Speed of the second half is $v_2 = 80$ km/h

Time to travel the first part is

$$t_1 = \frac{\frac{s}{2}}{v_1}$$

Time to travel the second part is

$$t_1 = \frac{\frac{s}{2}}{v_2}$$

The average speed

$$v = \frac{s}{t_1 + t_2}$$

In [1]:

s = 100
v_1 = 60
v_2 = 80
t_1 = (100/2)/v_1
t_2 = (100/2)/v_2
v = s / (t_1 + t_2)
print(f'The average speed is {v:.1f} km/h')

The average speed is 68.6 km/h

The average speed is not 70 km/h although the distances are equal, $t_1$ $<>$ $t_2$

سُوۡرَةُ حٰمٓ السجدة / فُصّلَت
ثُمَّ اسْتَوَىٰ إِلَى السَّمَاءِ وَهِيَ دُخَانٌ فَقَالَ لَهَا وَلِلْأَرْضِ ائْتِيَا طَوْعًا أَوْ كَرْهًا قَالَتَا أَتَيْنَا طَائِعِينَ ﴿١١
فَقَضَاهُنَّ سَبْعَ سَمَاوَاتٍ فِي يَوْمَيْنِ وَأَوْحَىٰ فِي كُلِّ سَمَاءٍ أَمْرَهَا ۚ وَزَيَّنَّا السَّمَاءَ الدُّنْيَا بِمَصَابِيحَ وَحِفْظًا ۚ ذَٰلِكَ تَقْدِيرُ الْعَزِيزِ الْعَلِيمِ ﴿١٢

Surah Fussilat: Thereafter turned He to the heaven and it was as smoke, and said Unto it and Unto the earth: come ye twain, willingly or loth. They said: we come willingly. (11) Then He decreed them as seven heavens in two days, and revealed Unto each heaven the command thereof; and We bedecked the nether heaven with lamps and placed therein a guard. That is the ordinance of the Mighty, the Knower. (12)

De hemelen en aarde (waren) een samenhangende massa. Wij hebben ze toen van elkaar gescheiden… Wij hebben de hemel tot een beschermend dak gemaakt … en de dag en de nacht, de zon en de maan geschapen. (Koran 41 11:12)