Algebra 1 Word Problem

Question

Two trains depart simultaneously from the same station, one traveling at a rate of 45 mph and the other traveling at 54 mph. How many hours before they are 495 apart if they travel in the opposite directions?

Answer 1

If the two trains are leaving from the same station and travelling in opposite directions, then their distances will get added together. You want to find the time t (hours) where the two distances add up to 495 miles.

Use the formula distance = rate x time to find the distance that each train travels in t hours. (Keep the variable for t, because it is the same for both trains, and it is the value the question is looking for.)

First train: d₁ = r₁t = 45t

Second train: d₂ = r₂t = 54t

Combined distance = d₁+ d₂ = 45t + 54t = 99t

Since you want the combined distance to be 495 miles, solve the algebraic equation to find the time t when that happens.

Hope this helps!

Answer 2

Distance equals Rate times Time

D=RT

Since the two trains depart at the same time their Time T will be the same

Distance of Train 1 is 45T

Distance of Train 2 is 54T

the total distance will be 495

so 45T+54T=495

99T=495

divide both sides by 99

T=5 hours