Trip planner problem. Why both give the correct result?

Question

Hi! Anybody, please, explain the difference. I solve the travel planner problem, where you need to find the travel time when you know the speed and distance. why do both expressions give the correct result?
minutes = distance / speed *60
minutes = distance/(40/60)

Answer 1

This post inspired me to create this code which is relevant to this discussion. 😂🤣
https://code.sololearn.com/ca4A19a13a69/?ref=app

Answer 2

oh no!
my bad...
a/(b/c) == a/b*c

Answer 3

Yaroslav Vernigora , what do you mean? Speed is known by the task description. What are your doubts?

Answer 4

speed === 40

Answer 5

because:
a/(b/c) == a*(c/b)

Answer 6

not VERY good...
but I have my basics ;)

Answer 7

Yaroslav Vernigora distance/speed *60=distance*60/speed
And distance /(40/60)=distance/40/60=distance/40*60

Answer 8

does the trip planner code coach have only once test?
if then, that mean that the value used for speed*60 should be equals to 40/60 ^^

Answer 9

that works also if speed is a constant and there are many tests ;P

Answer 10

yes, you are right, we have one constant - speed. it is equal to 40

Answer 11

🤭

Answer 12

visph no, wait... let's look at the first expression you wrote. I did not change the constant speed of 40 from 60. in one case, we multiply, in the second, we divide... and both expressions are correct! how can this be?

Answer 13

Simba you wrote
a/b/c = a*c/b
but I have written:
a / b * c == a / (b / c)

Answer 14

your first expression is a/b*c wich is evaluated as c*a/b coz left to right precedence (same precedence for / and *)
your second one is a/(b/c) wich is equal to a*(c/b) and equal to a*c/b or c*a/b or a/b*c

Answer 15

thank you very much! I'll need more time to figure this out. and repeat the priority of rolling out the operators

Answer 16

Thank y'all!

Answer 17

this is just maths ;)
n x * n
x * ------ == ------------
d d
and left to right precedence when same operators precedences

Answer 18

there is also the result in the correct answer in parentheses. if you remove them, the answer will be incorrect

Answer 19

I see, you very good know math! 👏👍

Answer 20

distance = 5
speed = 40
Example 1:
t = 5/40 × 60
1) 5/40 = 1/8
2) 1/8 × 60 = 60/8 = 15/2 = 7.5
Example 2:
t = 5 ÷ 40/60
1) 40/60 = 4/6 = 2/3
2) 5 ÷ 2/3 = 5 × 3/2 = 15/2 = 7.5
Check:
distance = 7.5 × 40 ÷ 60
1) 7.5 × 40 = 300
2) 300 ÷ 60 = 5
Conclusion:
example1 == example2