A journey of 700km partly by train and partly by bus. He started his journey at 8.00 a.m. by train which traveled at 50km/h. After alighting from the train, he took a lunch break of 30 minutes. He then continued his journey by bus which traveled at 75km/h. The whole journey took 11.5;hours .
Determine:
(i) the distance traveled by bus;
Time by train = (700-b)/50
Time by bus = b/75
(700 - b)/50 + b/75 = 11
50b + 52500 - 75b = 41250
- 25b + 52500 = 41250
-25b = 41250 - 52500
-25b = -11250
b = 450km
(ii) the time Makau started traveling by bus.
450/75
= 6 hours
= 8.00 + 11.30
= 1930h
= 1930 - 0600
= 1330
= 1.30 p.m
b) The bus developed a puncture after traveling 187.5km. It took 15 minutes to replace wheel. Find the time taken to complete the remaining part of the journey.
To find the time taken to complete the remaining part of the journey after the bus developed a puncture, we need to calculate the time it would take to travel the remaining distance at the bus's speed.
The distance traveled before the puncture is 187.5 km, so the remaining distance would be 450 km - 187.5 km = 262.5 km.
The bus travels at a speed of 75 km/h, so to find the time taken to travel the remaining distance, we divide the distance by the speed:
Time = Distance / Speed
Time = 262.5 km / 75 km/h
Time = 3.5 hours
However, we need to take into account the 15 minutes it took to replace the wheel. We convert 15 minutes to hours by dividing it by 60:
15 minutes / 60 = 0.25 hours
So the total time taken to complete the remaining part of the journey is 3.5 hours + 0.25 hours = 3.75 hours.
Therefore, the time taken to complete the remaining part of the journey is 3.75 hours.