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 11.5hours .

Determine:

(a) 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

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.

The first part of your solution is correct.

Since the puncture happened on the bus, and it happened after 187.5 km of the 450 km bus trip,
there were still 262.5 km to go,
at 75 km/h that would take
262.5/75 hours or 3.5 hours

To find the time taken to complete the remaining part of the journey, we need to calculate the distance remaining after the bus developed a puncture and the time it takes to travel that distance.

Distance remaining = Total distance - Distance traveled by bus before the puncture
Distance remaining = 700km - 187.5km
Distance remaining = 512.5km

Time taken to travel the remaining distance = Distance remaining / Speed of the bus
Time taken to travel the remaining distance = 512.5km / 75km/h

To convert kilometers to hours, we divide the distance by the speed:

Time taken to travel the remaining distance = 512.5km / 75km/h
Time taken to travel the remaining distance = 6.833 hours

Since we know that 1 hour is equal to 60 minutes, we can convert hours to minutes:

Time taken to travel the remaining distance = 6.833 hours * 60 minutes/hour
Time taken to travel the remaining distance = 410 minutes

However, we need to add the 15 minutes it took to replace the wheel:

Total time taken to complete the remaining part of the journey = Time taken to travel the remaining distance + Time taken to replace the wheel
Total time taken to complete the remaining part of the journey = 410 minutes + 15 minutes
Total time taken to complete the remaining part of the journey = 425 minutes

To find the time taken to complete the remaining part of the journey after the bus developed a puncture, first, we need to calculate the distance traveled before the puncture occurred.

Given that the bus traveled at a speed of 75 km/h and the time taken was 187.5 km, we can use the formula:

Time = Distance / Speed

Time before puncture = 187.5 km / 75 km/h

Time before puncture = 2.5 hours

Since it took 15 minutes to replace the wheel, we need to subtract this time from the remaining journey time of 11.5 hours.

Time remaining after the puncture = Total journey time - Time before puncture - Time taken to replace the wheel

Time remaining after the puncture = 11.5 hours - 2.5 hours - 0.25 hours

Time remaining after the puncture = 8.75 hours

So, the time taken to complete the remaining part of the journey is 8.75 hours.