A train travels a certain journey and is supposed to arrive at midday. When its average speed is 40km/h, it arrives at 1p.m. when its average speed is 48km/h it arrives at 11.a.m. What is the length of the journey
Let's first calculate the time difference between when the train arrives at 1 p.m. and 11 a.m.
The time difference is 1 p.m. - 11 a.m. = 2 hours.
Now, let's find the difference in travel time when the speed increases from 40 km/h to 48 km/h.
The difference in travel time = 2 hours.
Let's assume the length of the journey is L km.
At an average speed of 40 km/h, the travel time is L/40 hours.
At an average speed of 48 km/h, the travel time is L/48 hours.
The difference in travel time is L/40 - L/48 = 2 hours.
To solve this equation, we can find the least common multiple (LCM) of 40 and 48, which is 240. Multiply both sides of the equation by 240 to eliminate the fractions:
240*(L/40) - 240*(L/48) = 2 * 240.
6L - 5L = 480.
L = 480.
Therefore, the length of the journey is 480 km.