The problem asks for the number of days required to cover a new distance under modified conditions of rest and speed.
Step 1: Calculate Original Walking Time and Speed
First, determine the total time spent walking in the initial scenario.
- Total days = 80 days
- Rest per day = 10 hours
- Walking hours per day = 24 hours - 10 hours = 14 hours
- Total walking time = 14 hours/day * 80 days = 1120 hours
Now, calculate the original walking speed (S1).
- Distance = 1400 km
- Total walking time = 1120 hours
- Using the formula: Speed = Distance / Time
- S1 = $\\frac{1400 \\text{ km}}{1120 \\text{ hours}}$ = 1.25 km/hour
Step 2: Calculate New Speed and Walking Time Per Day
The problem states the new speed (S2) is 2.5 times the previous speed.
- S2 = 2.5 * S1 = 2.5 * 1.25 km/hour = 3.125 km/hour
Calculate the new walking hours per day.
- New rest per day = 16 hours
- New walking hours per day = 24 hours - 16 hours = 8 hours/day
Step 3: Calculate Total Walking Time Needed for New Distance
Determine the total time needed to cover the new distance at the new speed.
- New Distance = 1000 km
- New Speed (S2) = 3.125 km/hour
- Total walking time needed = New Distance / New Speed
- Total walking time needed = $\\frac{1000 \\text{ km}}{3.125 \\text{ km/hour}}$ = 320 hours
Step 4: Calculate the Number of Days Required
Finally, calculate the number of days required using the total walking time needed and the new walking hours per day.
- Total walking time needed = 320 hours
- New walking hours per day = 8 hours/day
- Number of Days = $\\frac{\\text{Total walking time needed}}{\\text{New walking hours per day}}$
- Number of Days = $\\frac{320 \\text{ hours}}{8 \\text{ hours/day}}$ = 40 days
Therefore, the man will cover 1000 km in 40 days.
Important Questions from Partial Speed
A train having length 210 metres takes 25 seconds to cross a 540 metres long bridge. How much time will the train take to cross a 630 metres long bridge?
A person X from a place A and another person Y from a place B set out at the same time to walk towards each other. The places are separated by a distance of 15 km. X walks with a uniform speed of 1.5 km / hr and Y walks with a uniform speed of 1 km / hr in the first hour, with a uniform speed of 1.25 km / hr in the second hour and with a uniform speed of 1.5 km / hr in the third hour and so on.
Which of the following is / are correct?
1. They take 5 hours to meet.
2. They meet midway between A and B.
Select the correct answer using the code given below:
The speed of a train is 120 kmph. What is the distance covered by it in 15 minutes?
I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways ?
Karan had covered two third of a certain distance when his car had a breakdown. He parked it and covered the remaining distance on foot. His time of travel on foot was 9 times his time of travel on car. What is the ratio of his walking speed with respect to his car’s speed?
