A train leaves the station at 5 am at 60 kmph. Another train leave the same station at 6:30 am at 75 kmph and travels in the direction of the first train. At what time and at what distance from the station will they meet?
Answers
Answer:
Step-by-speed = distance/time. For the trains to be at the same station at the same time, the distance must be the same for both.
Rearrange formula:
Distance = Speed x Time
For the early train: Distance = 60x Time. Therefore D= 60T
For the later train, the time taken is 1.5 hours less than the early train.
Therefore, D= 75 x (T-1.5)
Because they arrive at the same station at the same time, the distance must be the same for both, so the distance travelled by the first train must equal the distance travelled by the second train. The value of D must be the same for both.
75 x (T-1.5)= 60T
Multiply out the brackets:
75T- 75x1.5=60T
Rearrange the formula with T on one side and numbers on the other:
75T- 60T=112.5
15T=112.5
T=7.5 hours
Check:
Train 1 travelled for 7.5 hours at 60 km/h which equals 450 km. Arriving at 12.30pm
Train 2 travelled at 75 km/h for 6 hours which equals 450km, arriving at 12.30pm
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