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Brianna rides her bike then the bus and finally the train to visit her aunt. She rides her bike at 12 mph.
The bus travels at 28 mph while the train carries her at 246 mph. She rides the train for 15 minutes longer than she rides the bus.
She traveled 163 miles in 3 hours 30 minutes. How long was she riding her bike and 
riding on the bus?
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Let x be the time biking (in hours).
Let y be the time traveled by the bus (in hours).
Then the time traveled by the train is (y+0.25) hours. ( <<<---=== 0.25 = 0.25 of an hour = 15 minutes )
The total time equation is
x + y + (y+0.25) = 3.5 hours (1)
The total distance equation is
12*x + 28*y + 246*(y+0.25) = 163 miles (2)
These two equations, (1) and (2), are the math translation of the condition.
Simplify them and write the system of equations in the standard form.
x + 2y = 3.25 (1')
12x + 274y = 101.5 (2')
Then solve them by any method you want.
For example, you may use the Elimination method. For it, multiply eq(1') by 12 and then subtract it from the eq(2'). You will get
250y = 62.5 ====> y = 62.5/250 = 0.25.
Thus the time traveled by bus is 0.25 of of an hour = 15 minutes.
Then the time traveled by train is 15 + 15 = 30 minutes.
The time biking is the rest 3 hours 30 minutes minus 15 minutes minus 30 minutes = 2 hours and 45 minutes.
Check. The total distance is 12*2.75 + 28*0.25 + 246*0.5 = 163 miles. ! Correct !
Solved.
