Logical reasoning question

Sven is a keen cyclist and is riding from Alvros to Berget. At his normal cycling speed this will take him 30 minutes. His wife Helga will go by car to bring him and his bike back. They leave at the same time, but two thirds of the way between the two towns the car breaks down and Helga has to walk the rest of the way. The car goes at three times the speed Sven Cycles, but Helga walks at only one third of the speed he cycles.

Who arrives first and by how much (nearest min)

Helga by 12
Same time
Sven by 7
Sven by 33
Sven by 37

Hi everyone!

The answer is Sven by 7 minutes, this is the worked solution provided:

« If the car takes 10 minutes and breaks down 2/3 of the way in, it has taken 6.67 minutes before it breaks down.
Now the car would take 3.33 minutes to travel the rest of the distance, but Helga is 9 times as slow as the car so it takes her (9x3.33) = about 30 minutes. Add that to the 6.67 already travelled in the car, and she takes 36.67 minutes.
We know that Sven takes 30, so she takes roughly 7 minutes more. »

My question is: why is Helga 9 times as slow as the car???

Hello Juliette, that’s because Helga is 3 times slower than Sven (she would take 90 min in the whole trip), but Sven is 3 times slower than the car. So if you compare Helga directly to the car, she is 9 times slower.

Consider the time as “x”:

Car - x
Sven - 3x
Helga - 3x . 3 = 9x (she takes 9 times more than the car takes)

Good night from Brazil!

Obrigada pela tua ajuda!