We have the next given information:
- The first person climbs 10 feet every 30 seconds
- The second person climbs 5 feet every 15 seconds
1.
Set d for the distance(in feet) traveled by a climber t seconds after the first person starts climbing.
The first person starts to climb 15 seconds before the second climber.
For the first person:
Distance = speed * time
Where the speed = distance / time
Replacing
Speed = 10 feet / 30 seconds
Then
Speed = 1/3
Hence, we can write the next equation:
d1 = 1/3t
For the second climber:
He starts climbing 15 seconds after the first climber.
Distance = speed * time
Where
speed =5 feet / 15 seconds = 1/3
Then, we can write the next equation;
d2 = 1/3(t + 15)
2.
We need to find if the first climber is reached by the second climber.
It means that both distance equations must be equal.
d1 = d2
1/3t = 1/3(t -15)
Solve for t:
1/3t=(t+15)/3
3*1t= 3*(t+15)
3t = 3t - 45
3t-3t = -45
0 =- 45
In conclusion, both climbers have a rate of 1/3. However, the first climber has started 15 seconds before.
If both have the same speed, it means that the second climber won't catch up with the first climber.
Look at the next graph:
Where the color green represents the first climber and the color blue represents the second climber.
The y-axis represents the distance and the x-axis represents the time.
Look that the blue equation starts at x=15.
It means that the second climber starts after 15 minutes.