Question

1. the length of time, in hours, it takes a train to travel to city b varies inversely with the trains speed. the train carrie is traveling on is moving at a speed of 70 miles per hour, and it takes her 4 hours to arrive. if the train that steve is traveling on is moving at a speed of 50 mph, how long will it take him to arrive?

280 hours
87.55 hours
5.6 hours
2.6 hours

Explanation:

Step1: Define inverse variation

Let time = \( t \), speed = \( s \). Inverse variation: \( t = \frac{k}{s} \)

Step2: Find constant \( k \)

Given \( t=4 \), \( s=70 \): \( 4 = \frac{k}{70} \Rightarrow k=280 \)

Step3: Calculate new time

New \( s=50 \): \( t = \frac{280}{50}=5.6 \) hours

Answer:

5.6 hours