Gavin and Grace brother and sister jog to school every day G

Gavin and Grace, brother and sister, jog to school every day. Gavin jogs at 5 mph and Grace at 2 mph. When Gavin reaches school, Grace is 3/4 mile away. How far is the school from their home?

Solution

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