Algebra

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Algebra

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Two planes just took off from Boston Ma the first plane is traveling 1.5 times as fast as the second plane . After traveling in the same direction for 9 hours  they are 387 miles apart . What is the average speed of each plane ?
AlgebraHouse AlgebraHouse
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Re: Algebra

Assuming they left at the same time and are traveling in the same direction:

distance = rate x time

First Plane
d = rt
rate = 1.5r   {1.5 times as fast as second plane}
time = 9   {traveled for 9 hours}
d = 1.5r(9)   {distance = rate x time}
d = 13.5r

Second Plane
d = rt
rate = r  
time = 9   {traveled for 9 hours}
d = 9r   {distance = rate x time}

In 9 hours, the first plane will be 387 miles in front of second plane.

13.5r = 9r + 387   {first plane equals second plane plus 387}
4.5r = 387   {combined like terms}
r = 86   {divided each side by 4.5}
 
Rate of second plane is 86.

1.5r = rate of first plane
= 1.5(86)   {substituted 86, in for r, into 1.5r}
= 129   {multiplied}

129 mph is rate of first plane

- Algebra House