Question 271148
Rachel allows herself 1 hr to reach a sales appointment 50 mi away. After she has driven 30 mi, she realizes she must increase her speed by 15 mph in order to get there on time. What was her speed for the first 30 mi? 

FIRST HALF HOUR

let the speed she travelled for the first half hour be x mph
distance traveled in the first half hour will be 1/2 * x  MILES

SECOND HALF HOUR

SPEED FOR THE NEXT HALF HOUR WAS X+15 MPH

DISTANCE TRAVELLED WILL BE (X+15) *1/2  miles

the total distance she traveled was 50 miles

1/2*x + 1/2*(x+15) =50

x+x+15 = 2*50

2x= 100-15

x=85/2 = 42.5 mph.    In the second half hour it will be 42.5 +15 = 57.50 mph

Confirmation :

First half hour she travels 21.25 miles. In the second half hour she travels 28.75 miles.

the sum of these two is 50 miles.

Hope it is clear

Have fun with Math