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Train A and train b are leaving the station running on parallel tracks. Train A is scheduled to leave at 12:28 and train b is scheduled to leave 42 minutes later. Train A is scheduled to travel an average of 45 miles per hour and train b is scheduled to travel 55 miles per hour. When will train b catch train a? How far down the track?

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frika

Answer:

At 16:19

173.25 miles

Step-by-step explanation:

Train A:

Rate = 45 mph

Time = t hours

Distance traveled [tex]=45\cdot t[/tex] miles

Train B:

Rate = 55 mph

Time [tex]=t-\dfrac{42}{60}=t-\dfrac{7}{10}=t-0.7[/tex] hours

Distance traveled [tex]=55\cdot (t-0.7)[/tex] miles

The distances traveled are the same, so

[tex]45t=55(t-0.7)\\ \\45t=55t-38.5\\ \\45t-55t=-38.5\\ \\-10t=-38.5\\ \\10t=38.5\\ \\t=3.85[/tex]

Note that 3.85 hours is 3 hours 51 minutes. Then the train B will catch the train A at 16:19.

Each train will travel [tex]45\cdot 3.85=173.25[/tex] miles

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