2 passenger trains leave in opposite directions. The first train leaves at 10:00, going 100 km/hr. The second train leaves 2 hours later at 250 km/hr. What time will they be 300 km apart?
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The first train's distance from the start is equal to 100t, where t is the time after 10:00 in hours. The second train's distance from the start is equal to 250(t - 2), where t has the same meaning. So
100t + 250(t - 2) = 300
100t + 250t - 500 = 300 by applying the distributive property of multiplication over addition
100t + 250t = 300 + 500 by adding 500 to each side
350t = 800 by performing the additions on each side
t = 800 / 350 by dividing each side by 350
t = 2 2/7
2/7 of an hour is approximately 17 minutes, 14 seconds, so the two trains will be 300 km apart 2 hour, 17 minutes, and 14 seconds after 10:00, or 12:17:14.
100t + 250(t - 2) = 300
100t + 250t - 500 = 300 by applying the distributive property of multiplication over addition
100t + 250t = 300 + 500 by adding 500 to each side
350t = 800 by performing the additions on each side
t = 800 / 350 by dividing each side by 350
t = 2 2/7
2/7 of an hour is approximately 17 minutes, 14 seconds, so the two trains will be 300 km apart 2 hour, 17 minutes, and 14 seconds after 10:00, or 12:17:14.