Answer:
30 minutes
Step-by-step explanation:
We use the equation d = rt for this situation.
For the hiker, r = 3. The hiker also travels for an hour more than the cyclist; this means that in place of t, we use t+1. This gives us:
d = 3(t+1)
For the cyclist, r = 3+6 = 9. This gives us
d = 9t
Since they travel the same distance, we set them equal:
3(t+1) = 9t
Using the distributive property,
3(t)+3(1) = 9t
3t+3 = 9t
Subtract 3t from each side:
3t+3-3t = 9t-3t
3 = 6t
Divide both sides by 6:
3/6 = 6t/6
0.5 = t
It takes the cyclist 1/2 hour, or 30 minutes, to catch up.
