Mwangi and atieno live 60km apart mwangi leaves his home at 7:00am cycling towards otieno house at 20km/h otieno leaves his home at 8:00am cycling towards mwangi house at 8km/h
A)at what time did they meet
B)how far is the meeting point from mwangi house
C)a bus 18.8m long moving at 50km/h over takes a second bus moving at 45km/h in 30seconds find the length of the second bus
A) To find the time they met, we need to determine the time it takes for each person to travel from their respective homes to the meeting point.
For Mwangi:
Distance = Speed * Time
60 km = 20 km/h * Time
Time = 60 km / 20 km/h
Time = 3 hours
For Otieno:
Distance = Speed * Time
60 km = 8 km/h * Time
Time = 60 km / 8 km/h
Time = 7.5 hours
They both started at different times, so to find the time they met, we need to add the time it took for each person to travel.
Total time = 3 hours + 7.5 hours
Total time = 10.5 hours
Therefore, they met at 7:00 AM + 10.5 hours = 5:30 PM.
B) To find the distance between the meeting point and Mwangi's house, we need to determine the distance Mwangi traveled in the time it took for Otieno to reach the meeting point.
Distance = Speed * Time
Distance = 20 km/h * 7.5 hours
Distance = 150 km
Therefore, the meeting point is 150 km from Mwangi's house.
C) To find the length of the second bus, we can use the formula:
Distance = Speed * Time
The distance covered by the first bus is not given, so we cannot use that information. However, we know that the second bus was overtaken by the first bus in 30 seconds.
Distance covered by the second bus = Speed * Time
Distance covered by the first bus = (Speed of first bus + Speed of second bus) * Time
We can set up the equation:
18.8 m = (50 km/h + 45 km/h) * (30 s / 3600 s/h)
First, convert the time to hours:
30 s / 3600 s/h = 0.00833 h
18.8 m = (95 km/h) * (0.00833 h)
Now, convert the length of the second bus to meters:
18.8 m * 100 cm/m = 1880 cm
1880 cm = (95 km/h) * (0.00833 h)
Now, convert the speed from km/h to cm/h:
95 km/h * 100000 cm/km = 9500000 cm/h
1880 cm = 9500000 cm/h * (0.00833 h)
Simplifying:
1880 cm = 79135.5 cm
Therefore, the length of the second bus is approximately 1880 cm.
A) To find the time when Mwangi and Otieno meet, we can calculate the time it takes for each person to travel their respective distances.
Mwangi traveled a distance of 60km and he cycled at a speed of 20km/h. We can use the formula: Time = Distance / Speed to find the time taken by Mwangi.
Time taken by Mwangi = 60km / 20km/h = 3 hours (since distance and speed are in the same unit).
Otieno traveled a distance of 60km as well, but he cycled at a speed of 8km/h. We can calculate the time taken by Otieno using the same formula.
Time taken by Otieno = 60km / 8km/h = 7.5 hours.
Now, we need to find the total time passed from 7:00am until Otieno meets Mwangi. Otieno started cycling at 8:00am and took 7.5 hours to meet Mwangi.
So, the time when they meet is 8:00am + 7.5 hours = 3:30pm.
Therefore, they meet at 3:30pm.
B) To find the distance of the meeting point from Mwangi's house, we can calculate the distance traveled by Otieno before they meet.
From the calculation in question A, we know that Otieno cycled for 7.5 hours before they meet. At his speed of 8km/h:
Distance traveled by Otieno = 7.5 hours * 8km/h = 60km.
Since Otieno cycled for the same distance as Mwangi's house, the meeting point is at a distance of 60km from Mwangi's house.
C) To find the length of the second bus, we can use the formula: Distance = Speed * Time.
The first bus traveled a distance of 18.8m (convert to km by dividing by 1000) at a speed of 50km/h in 30 seconds.
Distance traveled by the first bus = 18.8m / 1000 = 0.0188km.
We know that time is given in seconds, so we need to convert 30 seconds to hours by dividing by 3600 (since there are 3600 seconds in an hour).
Time taken by the first bus = 30sec / 3600 = 0.00833 hours.
Let's assume the length of the second bus is "x" km. The second bus traveled at a speed of 45km/h for the same time (0.00833 hours) as the first bus.
Distance traveled by the second bus = 45km/h * 0.00833 hours = 0.37485 km.
Now we can set up an equation to find the value of "x":
0.37485 km - 0.0188 km = x km
0.35605 km = x km
Therefore, the length of the second bus is approximately 0.356 km, or 356 meters.