Chinn_asama wrote:
The distance between two stations A and B is 450 km. A train starts at 4 PM from A and moves towards B at an average speed of 60km/hr. Another train starts from B at 3.20 PM and move towards A at an avg.speed of 80km/hr. How far from A will the two trains meet and at what time?
I like to begin with a word equation. Here, I'll call the train leaving from station A the "A-train" and the other will be called the "B-train."
Since the total distance is 450 km, we can write:
(Distance the A-train travels) +
(Distance the B-train travels) = 450
Note: We'll start the clock at 4pm. So, at 4pm, the B-train has already been traveling for 40 minutes (i.e., 2/3 of an hour). So, at 4pm, the B-train has already traveled a distance of
(2/3)(80) km. In other words, the B-train has already traveled
160/3 km
Let's let t = the amount of time that has elapsed since 4pm.
We'll write:
(60t) +
(80t + 160/3) = 450
To solve, we'll simplify: 140t + 160/3 = 450
Multiply both sides by 3: 420t + 160 = 1350
Subtract 160 from both sides: 420t = 1190
Divide both sides by 420: t = 1190/420 = 119/42 hours
So, 119/42 hours after 4pm, the two trains meet. How far from Station A are they at this point?
Well, Train-A has been traveling at 60 kmh for 119/42 hours.
So, the distance from Station A will be (60)(119/42) km
(60)(119/42) = 170, So, the trains are 170 km from Station A.
Cheers,
Brent
