An executive traveling at 60 km hr would arrive 10 minutes early for an appointment, whereas at a speed of 45 km hr the executive would arrive 5 minutes early.how much time is there until the appointment?
T = Time until app.
60*(T-10/60) = 45*(T+5/60),
60T-10 = 45T + 3.75,
15T = 13.75, T = 0.91667 h = 55 Min.
To solve this problem, we can use the concept of relative speed.
Let's assume the distance to the appointment is represented by 'd' km.
Given that the executive travels at a speed of 60 km/h and arrives 10 minutes early, we can calculate the time taken to reach the appointment:
Time taken at 60 km/h = d/60 hours
Since the executive arrives 10 minutes early, the actual time taken to reach the appointment is:
Actual Time taken at 60 km/h = d/60 - 10/60 = (d-10)/60 hours
Similarly, when the executive travels at a speed of 45 km/h and arrives 5 minutes early, the actual time taken to reach the appointment is:
Actual Time taken at 45 km/h = d/45 - 5/60 = (d-5)/45 hours
Since both the actual times taken to reach the appointment are the same, we can equate the two expressions:
(d-10)/60 = (d-5)/45
To solve this equation, we can cross-multiply:
45(d-10) = 60(d-5)
Simplifying the equation gives:
45d - 450 = 60d - 300
Rearranging terms:
15d = 150
Dividing both sides by 15:
d = 10
So, the distance to the appointment is 10 km.
To find the time until the appointment, we need to consider the slower speed because it would take longer to cover the distance.
Time taken at 45 km/h = 10/45 hours = 2/9 hours
Converting this time to minutes:
2/9 * 60 minutes = 13.33 minutes (approximately)
Therefore, there is approximately 13.33 minutes left until the appointment.