- #1
kevinshen18
- 23
- 0
I was given this question from the Pascal Math contest 2001:
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Cindy leaves school at the same time every day. If she cycles at 20 km/h, she arrives home at 4:30 in the afternoon. If she cycles at 10 km/h, she arrives home at 5:15 in the afternoon. At what speed, in km/h, must she cycle to arrive home at 5:00 in the afternoon?
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This was how I attempted to solve it:
A difference in 10km/h (20km/h - 10km/h) results in her being 45 minutes late(5:15 - 4:30).
So I ratio it:
[tex] \frac{10km/h}{45min} = \frac{Xkm/h}{30min} [/tex]
If a difference of 10km/h results in a 45 minutes delay then what's the speed difference(X) that results in a 30 minutes delay(5:00 - 4:30).
I cross multiplied and got x = 6.6666...km/h.
Subtracting that from 20km/h my answer was 13.3333...km/h
The correct answer was 12 km/h.
Now I have no idea how I got it wrong but I would assume that the mistake was the speed to time ratio. Is it correct to do that? Can you even ratio speed and time or is that incorrect and not allowed? If it's not possible then why?
__________________________________________
Cindy leaves school at the same time every day. If she cycles at 20 km/h, she arrives home at 4:30 in the afternoon. If she cycles at 10 km/h, she arrives home at 5:15 in the afternoon. At what speed, in km/h, must she cycle to arrive home at 5:00 in the afternoon?
__________________________________________
This was how I attempted to solve it:
A difference in 10km/h (20km/h - 10km/h) results in her being 45 minutes late(5:15 - 4:30).
So I ratio it:
[tex] \frac{10km/h}{45min} = \frac{Xkm/h}{30min} [/tex]
If a difference of 10km/h results in a 45 minutes delay then what's the speed difference(X) that results in a 30 minutes delay(5:00 - 4:30).
I cross multiplied and got x = 6.6666...km/h.
Subtracting that from 20km/h my answer was 13.3333...km/h
The correct answer was 12 km/h.
Now I have no idea how I got it wrong but I would assume that the mistake was the speed to time ratio. Is it correct to do that? Can you even ratio speed and time or is that incorrect and not allowed? If it's not possible then why?