A train leaves the station at noon.  the train is 180 miles from its destination at 12:45 p.m. and 90 miles from its destination at 2:15 p.m. What is the equation to solve how far is the...

 A train leaves the station at noon.  the train is 180 miles from its destination at 12:45 p.m. and 90 miles from its destination at 2:15 p.m.

What is the equation to solve how far is the station from the destination?  Please also solve the equation.

What is the equation to solve what time will the train reach the destination? Please also solve the equation.

   Thank you

Asked on by marley112

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tiburtius's profile pic

tiburtius | High School Teacher | (Level 2) Educator

Posted on

I assume that the train is traveling at constant speed.

Between 12:45 pm and 2:15 pm the train has traveled 180-90=90 miles. So 90 miles in 1.5 hours which means that its speed is `90/1.5=60"mph."`

How far is the station from the destination?

`x=180+0.75*60=180+45=225"mi"`  

At 12:45 the train was 180 miles away from the station and by that time it has been traveling for 45 minutes (3/4 of an hour or 0.75 hours) at the speed of 60 mph.

At what time will the train reach the station?

`t=2.25+90/60=2.25+1.5=3.75=3:45"p.m."`

At 2:15 (that is 2.25 in decimal system) the train was 90 miles away from the station and was traveling at the speed of 60 mph.

Side note if we want to convert e.g. 6:20 into decimal system we simply take minutes and divide them by 60 (60 minutes in an hour). 

`6:25=6+20/60=6.333` 

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