A man leaves work at 5:00 and averages 30 mph on his 20 minute drive home. The man is picking up his wife for date night, a 6:00 dinner reservation. If the restaurant is twice as far from home as his workplace and they will average 60 mph to the restaurant, how much time do they have after he arrives home before they must leave?
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You could do the math to determine exactly how far away from home the workplace is (30 mph for 20 minutes is 10 miles), and then use that distance to find the time to the restaurant (multiply the 10 mile distance by 2 and use the 60 mph rate to determine the travel time to the restaurant). You would add the 2 travel times and then subtract that number from 60 (the time between leaving work and getting to the restaurant) to get the ‘left over time’ they would have at home.
An easier approach is to recognize that the speed from home to the restaurant is twice that of the speed from work to home. Since the distance is also twice as much, the travel time will be the same – 20 minutes for each drive (they must go twice as far, but are going twice as fast). So, with 60 minutes to get from work to home to the restaurant, and the driving time is 20 minutes from work to home and another 20 minutes from home to the restaurant, there are 20 minutes ‘left over’ at home between arrival and departure for the date night at the restaraunt.
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