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# Bus Journey Delays
A bus regularly travels from Cityville to Townsburg. On two separate occasions, the bus was delayed:
1. On the first trip, the bus traveled at an average speed of 45 km/h and arrived 20 minutes late.
2. On the second trip, the bus traveled at an average speed of 40 km/h and arrived 35 minutes late.
What is the distance between Cityville and Townsburg?
Let’s solve this step by step using the formula: distance = speed × time
1. Let t be the normal trip time in hours.
2. For the first trip:
– Time taken = t + 20/60 = t + 1/3 hours
– Distance = 45 × (t + 1/3)
3. For the second trip:
– Time taken = t + 35/60 = t + 7/12 hours
– Distance = 40 × (t + 7/12)
4. Since both trips cover the same distance:
45(t + 1/3) = 40(t + 7/12)
45t + 15 = 40t + 70/3
5t = 70/3 – 15
5t = 70/3 – 45/3
5t = 25/3
t = 5/3 hours = 100 minutes
5. Now we can calculate the distance using either trip:
Distance = 45 × (5/3 + 1/3) = 45 × 2 = 90 km
Therefore, the distance between Cityville and Townsburg is 90 km.
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