Numerical answer
Two trains start at the same time from stations P and Q, 360 km apart, and travel towards each other at constant speeds. After they meet, the train from P takes 4 hours to reach Q and the train from Q takes 9 hours to reach P. What is the speed, in km/h, of the train that started from P?
Show answer and solution
Answer: 36
Let the speeds be a (from P) and b (from Q), and let them meet after t hours.
After the meeting, train A covers the distance B had covered: a × 4 = b × t. Similarly b × 9 = a × t.
Dividing: 4a/(9b) = b/a ⇒ a²/b² = 9/4 ⇒ a : b = 3 : 2.
Multiplying: 36ab = abt² ⇒ t = √(4 × 9) = 6 hours.
So a + b = 360/6 = 60 km/h and a = 60 × 3/5 = 36 km/h (b = 24).
Tip: after meeting, a/b = √(t_B/t_A) and meeting time = √(t_A·t_B), where t_A, t_B are the post-meeting times.
After the meeting, train A covers the distance B had covered: a × 4 = b × t. Similarly b × 9 = a × t.
Dividing: 4a/(9b) = b/a ⇒ a²/b² = 9/4 ⇒ a : b = 3 : 2.
Multiplying: 36ab = abt² ⇒ t = √(4 × 9) = 6 hours.
So a + b = 360/6 = 60 km/h and a = 60 × 3/5 = 36 km/h (b = 24).
Tip: after meeting, a/b = √(t_B/t_A) and meeting time = √(t_A·t_B), where t_A, t_B are the post-meeting times.
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