Answers:
- slower train = 139 km per hour
- faster train = 159 km per hour
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Explanation:
x = rate of the slower train
x+20 = rate of the faster train
rates are in km per hour, abbreviated as kph
The train traveling at x kph will travel 5x km after 5 hours.
Use this formula
distance = rate*time
Using that same formula, the faster train travels 5(x+20) = 5x+100 kilometers in 5 hours.
The two distances must add to 1490 if we want the trains to pass by each other. Assume that the trains are traveling on parallel side-by-side tracks.
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So,
(slower train distance) + (faster train distance) = 1490
(5x) + (5x+100) = 1490
10x+100 = 1490
10x = 1490-100
10x = 1390
x = 1390/10
x = 139
The slower train moves at a rate of 139 km per hour.
x+20 = 139+20 = 159
The faster train moves at a speed of 159 km per hour.
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Check:
The slower train travels 139 kph and travels for 5 hours, so it covers a distance of 139*5 = 695 km
The faster train has a speed of 159 kph and travels for 5 hours, so it covers 159*5 = 795 km
Total distance = 695+795 = 1490
The answers are confirmed.
