2 runners(Alice, Bob) are running on the oval track at a constant speed. The tracklength is 200 meters.
First Alice ran with such low speed that Bob passed him every 2 minutes. To run faster than Bob, Alice sped up 2 times and now she is passing him every 6 minutes.
What speed did Bob ran at in km/h?
Solution:
How much was Bob faster than Alice at first speed?
1/30h is 2 minutes
x km/h * 1/30h = 0.2km
x = 6km/h
How much was Alice faster than Bob at second speed?
1/10h is 6 minutes
2x km/h * 1/10h = 0.2km
x = 1km/h
Don't know how to create equation out of this.
Best Answer
I wouldn't put $2x$ in the second equation. At that stage, you are still finding how much faster Alice is, not yet how fast Alice is. So if you omit $2$ you would find out that she was now faster by $2 km/h$.
Now it is time to set the equations. Let $A$ be Alice's original speed, $2A$ is her faster speed, let $B$ be Bob's speed, so you have:
$$B-A=6 km/h$$ $$2A-B=2 km/h$$
which gives you the solution ($A=8 km/h, B=14 km/h$).