Problem Set 6(Elizabeth's exercise)

Elizabeth visits her friend Andrew and then returns home by the same route. She always walks 4 kilometers per hour (km/h) when walking uphill, 8 km/h when walking downhill, and  6 km/h when walking on level ground. Suppose the path from Elizabeth’s home to Andrew’s home consists of ‘x’ meter in the level ground, ‘y’ meter in the uphill, ‘z’ meter in the  downhill and Elizabeth starts from home by 6 a.m. Write an algorithm and the subsequent Python code to determine when Elizabeth will reach Andrew’s home and when she will reach her home back if she spends ‘m1’ minutes in Andrew’s home. For example, if x is 1000, ‘y’ is 500, ‘z’ is 300  and m1 is ’30’ minutes, then Elizabeth takes 38 min to reach Andrew’s home so she will reach Andrew’s home by 6 hour 21 min. Elizabeth will take 19 min to walk from Andrew’s home to her home and time when will reach her home back is 7 hour 10 min.

The hour can be expressed in 12-hour format (not 24-hour format).  The minutes elapsed should be rounded down to the nearest integer.

Input Format

First line contains the distance ‘x’ in level ground

Next line contains the distance ‘y’ in uphill

Next line contains the distance ‘z’ in downhill

Next line contains the value for ‘ml’ minutes spent at Andrew’s home

Output Format

Print time by which Elizabeth will reach Andrew’s home. Print hours and minutes separated by a space

Print time by which Elizabeth will reach back her home. Print hours and minutes separated by a space

Input:

uphill,dowhill,level ground distances and time taken at andrew's house

Processing:

from math import ceil
x = int(input())
y = int(input())
z = int(input())
ml = int(input())

def time_taken(level,up,down):
    time = ceil(level*60/6000) + ceil(up*60/4000) + ceil(down*60/8000)
    return time

def time_clock(time_consumed):
    hrs = 6 + time_consumed//60
    minute = 0 + time_consumed%60
    if len(str(minute)) == 1:
        minute = '0' + str(minute)
    return hrs,minute

time_andrew = time_taken(x,y,z)
time_home = time_taken(x,z,y) + ml + time_andrew

Output:

Display the time when elizabeth meets Andrew and time when she returns home
Proof:

Program:

from math import ceil
x = int(input())
y = int(input())
z = int(input())
ml = int(input())

def time_taken(level,up,down):
    time = ceil(level*60/6000) + ceil(up*60/4000) + ceil(down*60/8000)
    return time

def time_clock(time_consumed):
    hrs = 6 + time_consumed//60
    minute = 0 + time_consumed%60
    if len(str(minute)) == 1:
        minute = '0' + str(minute)
    return hrs,minute

time_andrew = time_taken(x,y,z)
time_home = time_taken(x,z,y) + ml + time_andrew
print(time_clock(time_andrew)[0],time_clock(time_andrew)[1],sep = ' ')
print(time_clock(time_home)[0],time_clock(time_home)[1],sep = ' ')

Algorithm:

Step1. Get x,y,z and ml

Step2. Define the time taken function with three parameters level, up, down

Step2.1 assign time as the sum of level multiplied by 60/6000, up multiplied by 60/4000 and down multiplied by 60/8000

Step2.2 return time

Step3. Define time_clock function with one parameter time_consumed

Step3.1 assign hrs as the sum of 6 and the value obtained after dividing time_consumed by 60

Step3.2 assign minute as the sum of 0 and the value obtained which is the remainder when time_consumed is divided by 60

Step3.3 return hrs,minute

Step4. Call the time_taken function twice to calculate the time when she reached andrew’s home and when she returned home

Step5. Call the time_clock function twice get the time in the correct format and display the time

Step6. End