Mathematics: 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?

Answer6y x 5yStep-by-step explanation:...

Train a and train b are leaving the station running

davidsantos3121

16.01.2022

At 16:19

173.25 miles

Step-by-step explanation:

Train A:

Rate = 45 mph

Time = t hours

Distance traveled $=45\cdot t$ miles

Train B:

Rate = 55 mph

Time $=t-\dfrac{42}{60}=t-\dfrac{7}{10}=t-0.7$ hours

Distance traveled $=55\cdot (t-0.7)$ miles

The distances traveled are the same, so

$45t=55(t-0.7)\\ \\45t=55t-38.5\\ \\45t-55t=-38.5\\ \\-10t=-38.5\\ \\10t=38.5\\ \\t=3.85$

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 $45\cdot 3.85=173.25$ miles

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