Question

Ben and John both drive 40km from home to work each day. One day ben said to john, "If you drive home at your usual speed, I will average 40kmph faster than you and arrive in 20 minutes less time." find John's speed. Please show full working, thanx

Answer 1

Let Ben's speed be x and John's speed be y.
x=y+40
Time taken for each to drive 40 km:
Ben:
40/y = 40/(x+40)
John:
40/x

Time taken by Jonh is 20 minutes or 20/60 hours more than Ben
Therefore,
40/x=40/(x+40) +20/60
40/x=40/(x+40)+1/3
40(1/x - 1/(x+40))=1/3
40*(x+40-x)/((x+40)*x)=1/3
4800=x^2+40x
x^2+40x-4800=0
x=(-40+sqrt(1600+19200))/80
=(-40+sqrt(20800))/80
=(-40+40sqrt(13))/80
=(sqrt(13)-1)/2
y=x+40 = (sqrt(13)-1)/2 +40