SOLUTION: On Tuesday it took Julia Ward 2 h to drive 40 km and then make 3 round trips to a construction site. On Wednesday she drove 17 km and made 2 round trips to the site, all in 1 h. If

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: On Tuesday it took Julia Ward 2 h to drive 40 km and then make 3 round trips to a construction site. On Wednesday she drove 17 km and made 2 round trips to the site, all in 1 h. If      Log On


   

Question 96805This question is from textbook Algebra 2 and Trigonometry
: On Tuesday it took Julia Ward 2 h to drive 40 km and then make 3 round trips to a construction site. On Wednesday she drove 17 km and made 2 round trips to the site, all in 1 h. If all her driving was done at the same constant speed, what is the round-trip distance to the construction site? This question is from textbook Algebra 2 and Trigonometry

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

Let d=the round trip distance to the construction site
And r=her constant rate of speed
Distance(d)=Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
On Tuesday:
2hr=(40km+3d)/r------------------------eq1
On Wednesday:
1hr=(17km+2d)/r-----------------------eq2
Multiply both sides of each equation by r to get rid of fractions
2r=40+3d--------------------eq1
1r=17+2d---------------------eq2
Multiply each term in eq2 by 2
2r=34+4d-------------------------eq2
Subtract eq1 from eq2
0=-6+d add 6 to both sides
d=6 mi------------------------------round trip distance
CK
rate=(40+18)/2=58/2=29 mph
rate=(17+12)/1=29 mph

Hope this helps--ptaylor