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 ?

A) 192 mi

B) 208 mi

C) 216 mi

D) 224 mi

E) 272 mi

90+60/2=75 (average speed)

75*6/2=225(distance from Boston to NYC)

Solveit
Dec 14, 2015

#3**+15 **

We can use this formula to find the average rate of the the trip :

2 [ R_{1} * R_{2}] / [ R_{1} + R_{2 }] where R_{1} and R_{2} are the different rates over the same distance ....so we have

2[ 90 * 60] / [ 90 + 60] =

2[ 5400]/ [ 150] =

72 mph

So ......the average rate * 6 hrs = twice the distance......so divide this by 2 and we have

72 * 6 / 2 =

72 * 3 =

216 miles !!!

CPhill
Dec 14, 2015

#1**+10 **

I so wish i could help you! You're a very nice person :)

But i dont know how to do it..

I'm sorry :(

Hayley1
Dec 14, 2015

#3**+15 **

Best Answer

We can use this formula to find the average rate of the the trip :

2 [ R_{1} * R_{2}] / [ R_{1} + R_{2 }] where R_{1} and R_{2} are the different rates over the same distance ....so we have

2[ 90 * 60] / [ 90 + 60] =

2[ 5400]/ [ 150] =

72 mph

So ......the average rate * 6 hrs = twice the distance......so divide this by 2 and we have

72 * 6 / 2 =

72 * 3 =

216 miles !!!

CPhill
Dec 14, 2015

#5**+15 **

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

\(\frac{d}{90}=6-\frac{d}{60}\\~\\ 180*\frac{d}{90}=180*(6-\frac{d}{60})\\~\\ 2d=1080-3d\\~\\ 5d=1080\\~\\ d=216\; miles\)

Melody
Dec 14, 2015