word problem for mathematics

label Mathematics
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manuel traveled 3 hours nonstop to mexico, a total of 108 miles. he took a train part of the way, which averaged 40mph and then took a bus the remaining distance, which averaged 30mph. how long was manuel on the train 

May 18th, 2015

You can make two equations for this.

The first being 40x + 30y = 108

The second being x + y = 3 

In both of these cases x = train and y = bus

You solve for one variable, in this case I will solve for x out of the first equation. x = -3/4y + 27/10

Plug this into the second equation so -3/4y + 27/10 + y = 3

Simplified this is 1/4y + 27/10 = 3

Solve for y. y = 6/5

Plug this back into the first equation

40x + 30(6/5) = 108

Solve for x

x = 9/5

He was on the train for 9/5 hours, or 1.8 hours

I hope this helps! Please let me know if you have any questions!

May 18th, 2015

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