Question

Joe and Nancy decide to take a road trip. The first 72 miles of the drive are pretty easy, while the last 84 miles of the drive are filled with curves. They drove at an average 7 miles per hour faster for the first 72 miles of the trip. The entire trip took 3 hours. How fast were Joe and Nancy driving for the first 72 miles of the trip?

Answer 1

the answer the the problem would be 120

Answer 2

120

Explanation:

let r be the rate for the slower, 84 miles, portion of the trip

let t1 be the time for the 120 miles portion of the trip and t2 for the 84 miles portion

:

1) t1 + t2 = 3

2) (r+9)*t1 = 120 and r*t2 = 84

3) (r+9)*t1 + r*t2 = 120 + 84 = 204

:

expand the left side of equation 3

:

r*t1 + 9*t1 + r*t2 = 204

r*(t1+t2) +9*t1 = 204

:

substitute for (t1+t2) by using equation 1)

:

3*r + 9*t1 = 204

:

divide both sides of = by 3

:

4) r + 3*t1 = 68

:

use the equation for t1 from the equations defined at 2)

:

t1 = 120 / (r+9)

:

substitute for t1 in equation 4)

:

r + 3*(120/(r+9)) = 68

:

r^2 +9r +360 = 68 * (r+9)

:

r^2 -59r -252 = 0

:

(r-63)*(r+4) = 0

:

r = 63 and r = -4

:

we reject the negative value for r

:

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Joe and Nancy drove 63+9 = 72 miles per hour for the first 120 miles of the​ trip