Question 307801
Rachel allows hersef 1 hr to reach a sales appointment 50 mi away.  After she has driven 30 mi, she realizes that she must increase her speed by 15 mph in order to get there on time.  What was her speed for the first 30 mi?

Let her initial speed be x mph

time taken if she traveled that speed for 30 km  = 30/x

she increased her speed to by 15 mph

her new speed = x+15 mph
time taken by driving with new speed = 20/x+15 hours

Actual time taken = 30/x + 20/ x+15 hours
30/x + 20/ x+15 =1

lcm = x(x+15)

30(x+15)+20x= x(x+15)

30x+450 +20x= x^2 +15x

x^2+15x-30x-20x-450 =0
x^2-35x-450=0

x^2 -45x+10x-450=0
x(x-45)+10(x-45)=0

(x+10)(x-45)=0

x=-10 OR x =45

-10 is not valid

So she drove at 45 mph for 30 miles