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avatar+2496 

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)

 Dec 14, 2015

Best Answer 

 #3
avatar+104793 
+15

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

 

2 [ R1 * R2] /  [ R1 + R2 ]    where R1 and R2  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  !!!

 

 

 

cool cool cool

 Dec 14, 2015
 #1
avatar+8613 
+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 :(

 Dec 14, 2015
 #2
avatar+2496 
0

thanks Hayley! :)

 Dec 14, 2015
 #3
avatar+104793 
+15
Best Answer

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

 

2 [ R1 * R2] /  [ R1 + R2 ]    where R1 and R2  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  !!!

 

 

 

cool cool cool

CPhill Dec 14, 2015
 #4
avatar+2496 
0

But can it be determined without puting any distance

 Dec 14, 2015
 #5
avatar+105606 
+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

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

.
 Dec 14, 2015
 #6
avatar+105606 
0

Hang on a minute Solveit.  

What do you mean "without putting any distance" ?    indecision

 Dec 14, 2015
 #7
avatar+2496 
0

Thanks everybody, i understood everithing! exuse me for taking your times!

 Dec 14, 2015
 #8
avatar+2496 
0

My question it was wrong:  2 [ R1 * R2]  and d all of it distances (just a stupid question:)

 Dec 14, 2015

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