SOLUTION: Two trains depart towards from two stations which distance is 900 km and meet in the middle of the distance. The departure of the first train is 1 hour

Question 1040972: Two trains depart towards from two stations which distance is 900 km
and meet in the middle of the distance. The departure of the first train is 1 hour
later than the departure of the second train but it�s speed is 5 km/hour greater.
Find the speed of each of trains.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = distance.
each train travels 450 kilometers.
r = rate
t = time
d = distance
r*t = d
since d = 450, then r*t = 450
that would be the formula for the first train.
the second train travels one hour less but 5 kilometers per hour faster.
formula for second train is (r+5)*(t-1) = 450
since they both travel the same distance of 450 kilometers, set r*t = (r+5)*(t-1)
simplify to get r*t = r*t - r + 5*t - 5
subtract r*t from both sides of the equation to get 0 = -r + 5*t - 5
multiply both sides of the equation by -1 to get 0 = r - 5*t + 5
add 5*t to both sides of the equation to get 5*t = r+5
divide both sides of the equation by 5 5 to get t = (r+5)/5
replace t with (r+5)/5 in the equation of r*t = 450 to get r*(r+5)/5 = 450
multiply both sides of the equation by 5 to get r*(r+5) = 2250
simplify to get r^2 + 5*r = 2250
subtract 2250 from both sides of the equation to get r^2 + 5*r - 2250 = 0
factor this quadratic equation to get (r+50)*(r-45) = 0
solve for r to get r = -50 or r = 45.
r can't be negative, so r = 45.
replace r with 45 in the equation of r*t = 450 to get 45*t = 450.
solve for t to get t = 10.
first train travels for 10 hours at 45 miles per hour to travel 450 miles.
second train travels for 9 hours at 50 miles per hour to travel 450 miles.
total distance traveled by both trains together is 900 miles.
they meet at exactly the same time.
for example:
first train starts as 0900 hours (9:00 am) and travels for 10 hours to reach 450 mile distance at 1900 hours (7:00 pm).
second train starts at 1000 hours (10:00 am) and travels for 9 hours to reach 450 miles distance at 900 hours (7:00 pm).
everything checks out as far as i can tell.
first train travels at 45 kilometers per hour and second travels at 50 kilometers per hour is the solution.

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