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Zorluk: OrtaRate, Time, and Distance Problems

An express cargo train leaves Station A heading toward Station B at a constant speed of 5050 miles per hour. At the exact same time, a local freight train leaves Station B heading toward Station A along a parallel track at a constant speed of 3030 miles per hour. If the total distance between Station A and Station B is 360360 miles, how many miles from Station A will the two trains meet?

Cevap: 225 miles

Cevap

The two trains will meet 225 miles from Station A.
When two objects move directly toward each other, their rate of approach is the sum of their speeds (50+30=8050 + 30 = 80 mph). Covering the total distance of 360360 miles at a rate of 8080 mph takes 4.54.5 hours. In 4.54.5 hours, the train traveling from Station A at 5050 mph covers a distance of 50×4.5=22550 \times 4.5 = 225 miles.

Adım Adım Çözüm

1
Calculate the combined relative speed of both trains.
Relative speed = 50+30=8050 + 30 = 80 miles per hour.
Since the two trains move toward each other, their relative rate of convergence is the sum of their individual speeds.
2
Calculate the time required for the two trains to meet.
Time t=360 miles80 mph=4.5t = \frac{360 \text{ miles}}{80 \text{ mph}} = 4.5 hours.
Time equals total distance divided by combined relative speed.
3
Calculate the distance covered by the express train from Station A.
Distance = 50 mph×4.5 hours=22550 \text{ mph} \times 4.5 \text{ hours} = 225 miles.
Distance equals the rate of the train departing Station A multiplied by the elapsed time.

Anahtar Kavram

Relative speed of converging objects moving toward each other
Tahmini Süre:1m 30s
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Rate, Time, and Distance Problems

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