Two bicyclists are 180 miles apart when they start racing towards each other. If their speeds are 14 mph and 16 mph respectively, how long will it be before they are twenty miles apart?

5.3 hours, or 319.999 or 320 minutes

Explanation:

If the bicyclists are 20 miles apart, they have travelled 160 miles in total because:

180 - 20 = 160

Make an equation for the bicyclists traveling 160 miles total:

14x + 16x = 160

Solve for x:

14x + 16x = 160

30x = 160

30x : 30 = 160 : 30

x = 5.3

So after 5.3 hours, both bicyclists have traveled 160 miles, and are 20 miles apart.

5.3 hours in minutes is

60 • 5.3 = 319.99 or 320 minutes.

So first what you want to do is find out how much closer they would be after one hour. Since they're both moving towards each other, that means they gain,

14 + 16 = 30 m in one hour.

(because they're both moving towards each other, so for the amount they get closer to each other, you want to add both of their speeds)

Since they were originally 180 miles apart, and you want to find how long it would take for them to be 20 miles apart, you want to just subtract 20 from 180 to find the total distance they have to travel.

180 - 20 = 160

Now divide 160 by 30 to find out how many sets of 30 miles, or one hour time periods, there are in 160 miles.

160 / 30 = 16/3 hours.

To make this into minutes, you can just multiply by 60.

16/3 * 60 = 960/3

960/3 = 320

So it'll be 320 minutes before they are 20 miles apart.