Mandys communte to work in the morning takes 45 minutes and

Mandy\'s communte to work in the morning takes 45 minutes and coming home she is able to drive 10 miles per hour faster, so it only takes 30 minutes, how far is her communte (one-way)?

Solution

let her speed of travel going to work be =x
on return she drives 10 mph faster.hence her return speed =x+10
let the distance of home to work =d=distance of work to home
using the formula d=rt...or t=d/r...
time of travel to work =d/x=45/60..or d=x*45/60=3x/4...(1)
time of travel to home =d/(x+10)=30/60..or d=(x+10)30/60=(x+10)/2..(2)
equating d from the 2 eqns.
d=3x/4=(x+10)/2..crossmultiplying
2*3x=4*(x+10)
6x=4x+40
6x-4x=40
2x=40
x=20 mph
d=3x/4=3*20/4=15 miles.