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distance(d)=rate(r) times time(t) or d=rt
Let d= distance to school
So distance Gavin jogs is Gavin's rate (5 mph) times time(t) and this equals d.
And distance Grace jogs is Grace's rate (2 mph) times time(t) and this equals (d-3/4)
So our two equations are :
d=5t or t=d/5-----------------------------------eq 1
(d-3/4)=2t or t=(d-3/4)/2---------------------------eq 2
substitute t=d/5 into equation 2
d/5=(d-3/4)/2 multiply both sides by 10
2d=5(d-3/4) get rid of parens
2d=5d-15/4 subtract 5d from both sides
2d-5d=-15/4
-3d=-15/4 divide both sides by -3
d=5/4 or 1.25 mi------------------------distance to school
CK
t=d/r
It takes Gavin 1.25/5=0.25 hr to go to school
It takes grace 1.25-3/4=1.25-.75=0.5 mi/2 =0.25 hr to get 3/4 mi away from school
Hope this helps----ptaylor
