Makau made a journey of 700km partly by train and party by bus. He started his journey at 8:00am by train which traveled at 50km/h ,after he alighted he took a launch break of 30mins.he then took a bus which traveled at 75km/h.the whole journey took 11and 1/4 hours (a)determine (I) the distance traveled by bus (ii) the time makau started traveling by bus.(b) the bus had a puncture after travelling for 187.5km it took 15mins to replace the wheel find the time taken to complete the remaing part of the journey
a)487.5km
b)12:45pm
c)3hrs 45mins
To solve this problem, let's break it down step by step:
(a) Determining the distance traveled by bus:
1. Start by finding the total distance traveled for the entire journey. Makau traveled a total of 700km.
2. Assume Makau traveled "x" kilometers by train. Since the total distance is 700km, the distance traveled by bus would be 700 - x kilometers.
3. Now, let's calculate the time it took Makau to travel by train. The speed of the train was 50km/h, and the train journey took some time before Makau alighted and took a break.
Time taken to travel by train = Distance / Speed = x / 50
4. Since Makau took a launch break of 30 minutes, we need to include this break time in our calculations.
Total time taken for the train journey = x / 50 + 30 minutes
5. The time taken for the bus journey is the remaining time after the train journey, which adds up to 11 and 1/4 hours (45/4 hours).
Total time taken for the bus journey = 45/4 hours - (x / 50 + 30 minutes)
6. We can convert the remaining time taken for the bus journey to minutes for easier calculation.
Total time taken for the bus journey = 45/4 * 60 - (x / 50 + 30) minutes
7. Now, let's equate the total distance traveled with the sum of the distances traveled by train and bus:
Total distance traveled = Distance traveled by train + Distance traveled by bus
700 = x + (700 - x)
Simplifying the equation, we get:
700 = 2x
x = 350
So, Makau traveled 350km by train and the remaining distance traveled by bus would be:
Distance traveled by bus = 700 - 350 = 350km
8. Therefore, the distance traveled by bus is 350km.
(b) Determining the time Makau started traveling by bus:
1. We know that Makau started his journey at 8:00 am.
2. The train journey took some time before the break. So, we need to calculate the time taken for the train journey.
Time taken for the train journey = Distance / Speed = 350km / 50km/h = 7 hours
3. Since Makau took a 30-minute break after the train journey, the time when he starts traveling by bus would be:
Time for bus journey to start = 8:00 am + 7 hours + 30 minutes = 3:30 pm
Therefore, Makau started traveling by bus at 3:30 pm.
(c) Determining the time taken to complete the remaining part of the journey after the bus puncture:
1. The bus had a puncture after traveling for 187.5km.
2. It took 15 minutes to replace the wheel.
3. To find the time taken to complete the remaining part of the journey, we need to subtract the time taken for the puncture and the wheel replacement from the total travel time.
Remaining time for the journey = Total travel time - Time taken for puncture and wheel replacement
Remaining time for the journey = 45/4 hours - 15 minutes
Converting 45/4 hours to minutes: 45/4 * 60 = 337.5 minutes
Therefore, the time taken to complete the remaining part of the journey would be:
Remaining time for the journey = 337.5 minutes - 15 minutes = 322.5 minutes.