Math Games

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Question: Trouble with a math reasoning problem?

Joseph drove from his house to the football game at an average rate of 50 miles per hour. Because of traffic jams, he drove home from the football game along the same route at an average rate of only 35 miles per hour. If his total driving time to the game and back from the game equaled 3 hours and 24 minutes, then how many total miles did he drive?

I understand the problem but I'm having trouble figuring out the answer. Please help and show your work.

Answer: The distance is the same in both directions. So, let's call the distance d.

To the game, he drove d miles at 50 miles per hour, so it took d/50 hours to get there. On the way home, it took d/35 hours.

24 minutes is 24/60 hours, or .4 hours, so 3 hours 24 minutes is 3.4 hours.

d/50 + d/35 = 3.4 Multiply by the LCM of 50 and 35, which is 350:

7d + 10d = 1190
17d = 1190
d = 70 miles

BUT d is the distance one way, so in total he drove 2d or 140 miles.

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