Question 73261

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