a person was climbing on a building.he slips 1 metre for every 5 metre he climb up. if the building is 53 metre high and he takes 5 seconds to climb 1 metre,find the total time taken by him to get on the top of the building.
d = 53 + 53/5 = 63.6 m.
T = d/r = 63.6/5 = 12.72 s.
To find the total time taken by the person to reach the top of the building, we need to calculate two components: the time taken to climb up and the time taken to slip down.
Let's break down the problem step by step:
1. Calculate the number of times the person slips while climbing up the building:
- For every 5 meters climbed, the person slips down 1 meter.
- So, the person slips down a total of 53/5 = 10.6 times.
- Since the person cannot slip a fraction of a time, let's round this down to 10 times.
2. Calculate the distance the person effectively climbs:
- The total distance climbed is 53 meters.
- Since the person slips down 1 meter for every 5 meters climbed, the effective distance climbed can be calculated by subtracting the slips from the total distance.
- Effective distance climbed = Total distance climbed - Slips down
= 53 meters - (10 slips x 1 meter per slip)
= 53 meters - 10 meters
= 43 meters.
3. Calculate the time taken to climb up:
- The person takes 5 seconds to climb 1 meter, so the time taken to climb up 43 meters can be calculated by multiplying the time taken to climb 1 meter by 43.
- Time taken to climb up = Time taken to climb 1 meter x Distance climbed
= 5 seconds/meter x 43 meters
= 215 seconds.
4. Calculate the time taken to slip down:
- Since the person slips 1 meter for every 5 meters climbed, the time taken to slip down can be calculated by multiplying the time taken to climb 1 meter by the number of slips.
- Time taken to slip down = Time taken to climb 1 meter x Number of slips
= 5 seconds/meter x 10 slips
= 50 seconds.
5. Calculate the total time taken:
- The total time taken is the sum of the time taken to climb up and the time taken to slip down.
- Total time taken = Time taken to climb up + Time taken to slip down
= 215 seconds + 50 seconds
= 265 seconds.
Therefore, the person takes a total of 265 seconds to reach the top of the building.