After traveling 60 km, a train crashed. so she completed the next jour...
Problem Statement
A train travels 60 km and then crashes. After that, it completes the next journey at 2/3 of its original speed. As a result, it reaches its destination 40 minutes late. If the accident had happened 30 km further, it would have been only 20 minutes late. What is the total speed of the train and the total distance traveled?
Solution
Let's assume that:
- x is the speed of the train before the accident
- y is the distance traveled by the train before the accident
- t1 is the time taken by the train to travel the distance y before the accident
- t2 is the time taken by the train to travel the remaining distance after the accident
- t3 is the time taken by the train to travel the additional 30 km after the accident
- d1 is the distance traveled by the train after the accident before the additional 30 km
- d2 is the total distance traveled by the train
Calculating the speed of the train after the accident
The speed of the train after the accident is 2/3 of its original speed. Therefore:
x2 = (2/3) * x
Calculating the time taken to travel the remaining distance after the accident
The time taken to travel the remaining distance after the accident can be calculated as:
t2 = (y - 60) / x2
Calculating the time taken to travel the additional 30 km after the accident
The time taken to travel the additional 30 km after the accident can be calculated as:
t3 = 20 / 60 = 1/3 hours
Calculating the time taken to travel the distance before the accident
The time taken to travel the distance before the accident can be calculated as:
t1 = 60 / x
Calculating the distance traveled by the train after the accident before the additional 30 km
The distance traveled by the train after the accident before the additional 30 km can be calculated as:
d1 = t2 * x2
Calculating the total distance traveled by the train
The total distance traveled by the train can be calculated as:
d2 = y + d1 + 30
Calculating the time taken to travel the total distance
The time taken to travel the total distance can be calculated as:
t = t1 + t2 + t3
Calculating the speed of the train
The speed of the train can be calculated as:
x = d2 / t
Calculating the