A man drives fom the origin to his destination in his car at the speed of 24km/hr and reaches 5 minutes late.Next day he drives from the same origin to the same destination with a speed of 30km/hr and reaches 4 minutes early.Find at what distance is the origin from the destination.Write a linear equation using the given information.
time difference is 9 minutes = 9/60 hr
the distances are the same
time = distance/speed
d/24 = d/30 + 9/60
d = 18
check:
18/24 = 3/4 = 45 min
18/30 = 3/5 = 36 min
To find the distance between the origin and the destination, we need to first understand the concept of speed, time, and distance.
Speed is defined as the distance traveled per unit of time. In this case, the man traveled at a speed of 24 km/hr and 30 km/hr on two different days.
Time is the duration it takes to travel a certain distance. In this case, the man reached the destination 5 minutes late on the first day and 4 minutes early on the second day.
Distance is the total amount of space covered between the origin and the destination.
Let's calculate the distance using the given information.
On the first day, the man traveled at a speed of 24 km/hr. Since he reached 5 minutes late, we can convert this to hours by dividing 5 minutes by 60 (1 hour = 60 minutes).
5 minutes = 5/60 hours
Now, we can calculate the distance using the equation:
Distance = Speed × Time
Distance = 24 km/hr × (Time + 5/60 hours)
On the second day, the man traveled at a speed of 30 km/hr. Since he reached 4 minutes early, we can convert this to hours by dividing 4 minutes by 60 (1 hour = 60 minutes).
4 minutes = 4/60 hours
Now, we can calculate the distance using the equation:
Distance = Speed × Time
Distance = 30 km/hr × (Time - 4/60 hours)
Since the distance remains the same on both days, we can equate the two equations:
24 × (Time + 5/60) = 30 × (Time - 4/60)
Now, we can solve this equation to find the value of the Time:
24Time + 24(5/60) = 30Time - 30(4/60)
24Time + 1 = 30Time - 2
Subtracting 24Time from both sides:
1 = 6Time - 2
Adding 2 to both sides:
3 = 6Time
Dividing by 6 on both sides:
Time = 0.5 hours
Now that we have found the value of Time, we can substitute it into either of the earlier equations to find the distance (Distance = Speed × Time). Let's use the first equation:
Distance = 24 km/hr × (0.5 hours + 5/60 hours)
Distance = 24 km/hr × (0.5 + 5/60) hours
Distance = 24 km/hr × (0.5 + 1/12) hours
Simplifying the equation:
Distance = 24 km/hr × (6/12 + 1/12) hours
Distance = 24 km/hr × (7/12) hours
Distance = 14 km
Therefore, the distance between the origin and the destination is 14 kilometers.
The linear equation using the given information is:
24 × (Time + 5/60) = 30 × (Time - 4/60)
where Time represents the duration of the journey in hours.