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# Where is my mistake ?

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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
+80935
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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  !!!

CPhill  Dec 14, 2015
Sort:

#1
+8623
+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
#2
+2493
0

thanks Hayley! :)

Solveit  Dec 14, 2015
#3
+80935
+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  !!!

CPhill  Dec 14, 2015
#4
+2493
0

But can it be determined without puting any distance

Solveit  Dec 14, 2015
#5
+91435
+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
#6
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Hang on a minute Solveit.

What do you mean "without putting any distance" ?

Melody  Dec 14, 2015
#7
+2493
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Thanks everybody, i understood everithing! exuse me for taking your times!

Solveit  Dec 14, 2015
#8
+2493
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My question it was wrong:  2 [ R1 * R2]  and d all of it distances (just a stupid question:)

Solveit  Dec 14, 2015

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