Jason S. answered • 03/29/15

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This is a problem about finding the intersect of linear equations. So, if we consider the distance traveled by car one as a function of time,

d(t) = speed * t

then we have

d1( t ) = 50 * time

d2( t ) = 30 * time

d(t) = speed * t

then we have

d1( t ) = 50 * time

d2( t ) = 30 * time

We are looking for a specific case with these. We can the point where the distance traveled by the first car (d1) is 15 miles greater than the distance traveled by the second car (d2)

d1( t ) = d2 ( t ) + 15

If we take the equations for d1 and d2, and substitute them in, then we get (including units now)

50 m/hr * t hr = 30 m/hr * t hr + 15 m

d1( t ) = d2 ( t ) + 15

If we take the equations for d1 and d2, and substitute them in, then we get (including units now)

50 m/hr * t hr = 30 m/hr * t hr + 15 m

which we solve with a bit of algebra (solve for t).

50 m/hr * t hr - 30 m / hr * t hr = 30 m/hr * t hr - 30 m/hr * t hr + 15 m

( 50 m/hr - 30 m / hr ) * t hr = ( 30 m/hr * t hr - 30 m/hr * t hr ) + 15 m

(20 m / hr) * t hr = 0 + 15 m

20 m / hr * t hr =15 m

t hr = (15 m ) / (20 m / hr )

t hr = (15 m ) / (20 m / hr )

t hr = (15 m * hr ) / 20 m

t hr = (15 / 20 ) hr

t = .75 hr = 45 minutes

t = .75 hr = 45 minutes

Holmes F.

03/29/15