Answer:
120
Step-by-step 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
