N city is 635 k.m. away from F city. Mr.L set off from N city to F city at 8:20 am at a speed of 70km/h. Mr.G left from f city to N city 30 min later at speed of 80km/h. At what time did they pass each other? (Both trveling on same road.)
They started out BOTH traveling towards each other at 8:50 AM, at which time Mr. L had already traveled 70/2 = 35 km, so they were 600 km apart then. The distance between them decreased at a rate of 80 + 70 = 150 km/h. Therefore they met 4 hours later, at 12:50 PM
To find out at what time Mr.L and Mr.G passed each other, we need to determine the time it took for each of them to travel the distance between the cities.
Let's start by finding the time it took for Mr.L to travel from N city to the point of passing.
Distance = Speed x Time
Given that the distance between N city and F city is 635 km, and Mr.L traveled at a speed of 70 km/h, we can write:
635 km = 70 km/h x Time
Dividing both sides of the equation by 70 km/h:
Time = 635 km / 70 km/h
Time = 9.07 hours
So, it took Mr.L approximately 9.07 hours to reach the point of passing.
Now, let's find the time it took for Mr.G to travel from F city to the point of passing.
Given that Mr.G left from F city 30 minutes (or 0.5 hours) later than Mr.L, we need to subtract this time from the total time it took for Mr.L to reach the point of passing.
Total Time for Mr.G = Time for Mr.L - Delay
Total Time for Mr.G = 9.07 hours - 0.5 hours
Total Time for Mr.G = 8.57 hours
Now, we can calculate the distance traveled by Mr.G using his speed of 80 km/h:
Distance = Speed x Time
Distance = 80 km/h x 8.57 hours
Distance = 685.6 km
Since Mr.G is traveling towards N city from F city, the combined distance traveled by both Mr.L and Mr.G should add up to 635 km.
Distance traveled by Mr.L + Distance traveled by Mr.G = 635 km
685.6 km + Distance traveled by Mr.L = 635 km
Distance traveled by Mr.L = 635 km - 685.6 km
Distance traveled by Mr.L = -50.6 km
However, we cannot have a negative distance in this case. The negative value indicates an error in the calculations, most likely from rounding numbers.
Hence, we need to recalculate.
Given that both Mr.L and Mr.G are traveling towards each other, we can assume that the distance traveled by each of them is the same when they meet.
So, the distance traveled by Mr.L = Distance traveled by Mr.G
Let's denote the distance traveled by Mr.L as D.
D = 70 km/h x Time for Mr.L = 70 km/h x 9.07 hours = 635.9 km (rounded to one decimal place)
Using the same logic, the distance traveled by Mr.G is also approximately 635.9 km.
Now, we can calculate the time it took for Mr.G to reach the passing point.
Time for Mr.G = Distance traveled by Mr.G / Speed of Mr.G
Time for Mr.G = 635.9 km / 80 km/h = 7.95 hours (rounded to two decimal places)
Since Mr.G left from F city 30 minutes later than Mr.L, we need to add this time to the time it took for Mr.G to reach the passing point.
Total Time for Mr.G = Time for Mr.G + Delay
Total Time for Mr.G = 7.95 hours + 0.5 hours = 8.45 hours (rounded to two decimal places)
Therefore, Mr.G passed Mr.L approximately 8 hours and 27 minutes (rounded to the nearest minute) after Mr.L started his journey.
To find the time they passed each other, we need to add the delay of 30 minutes to the start time of Mr.L.
Passing Time = Start Time of Mr.L + Total Time for Mr.G
Start Time of Mr.L = 8:20 am
Total Time for Mr.G = 8.45 hours (converted to minutes) = 507 minutes (rounded to the nearest minute)
Passing Time = 8:20 am + 507 minutes
Adding 507 minutes to 8:20 am, we get:
Passing Time = 8:20 am + 507 minutes = 8:20 am + 8 hours and 27 minutes
Calculating the passing time, we get:
Passing Time = 8:20 am + 8 hours and 27 minutes = 4:47 pm
Therefore, Mr.L and Mr.G passed each other at approximately 4:47 pm.