Solve. You must show equation

Question

The distance between two towns consists of two stretches of road whose lengths are consecutive integers. A man drives on the shorter stretch at 60 mph and on the rest at 46 mph, so that his average rate for the whole trip is 52 mph. Find the total distance of the trip using the formula distance = rate • time.

Answer 1

d=r*t

d/r=t

x and x+1 are the distances

x/60=time for shorter stretch

(x+1)/46=time for longer stretch

total distance=rate*total time

x+(x+1)=52([x/60]+[(x+1)/46])

2x+1=(52x/60)+[52(x+1)]/46

2x+1=(52x/60)+(52x+52)/46

2x+1=52x/60+52x/46+52/46

simplify

2x+1=13x/15+26x/23+26/23

multiply all terms by the LCM of 15*23=345

345(2x)+345(1)=345(13x/15)+345(26x/23)+345(26/23)

690x+345=299x+390x+390

690x+345=689x+390

690x-689x=390-345

x=45 miles

x+1=46 miles

total distance=45+46=91 miles