Steve travels from NYC to Boston at 90mph and returns to NYC at 60mph taking 6 hours total for the round-trip without stopping. What is the distance between NYC and Boston ?
Let the distance be d
Let x be the time to get there and y be the time to get back
x+y=6
y=(6-x)
speed=distance/time
90=d/x 60=d/(6-x)
90x=d 60(6-x)=d
x=d/90 (1) 6-x = d/60
x=6 - d/60 (2)
so
\(\frac{d}{90}=6-\frac{d}{60}\\~\\ 180*\frac{d}{90}=180*(6-\frac{d}{60})\\~\\ 2d=1080-3d\\~\\ 5d=1080\\~\\ d=216\; miles\)
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