D=70*X+1+50*X

Question

LAURA DRIVES ALONG A HIGHWAY AT 70MPH UNTIL SHE ENCOUNTERS HEAVY TRAFFIC AND HAS TO SLOW TO 50MPH. THE TIME SHE DROVE AT 70MPH IS 1 HOUR MORE THAN THE TIME SHE DROVE AT 50MPH AND THE DISTANCE SHE DRAVE AT 70MPH IS GREATER THAN THE DISTANCE SHE DROVE AT 50MPH. IF THE DIFFERENCE IN THE DISTANCE SHE DROVE AT 70MPH AND 50MPH IS 100 MILES. DETERMINE THE TIME SHE SPENT DRIVING AT EACH SPEED.

Answer 1

alredee did this

time at 50=(1/4)our...15 minuts

so time at 70=1.75 ours

Answer 2

Let the time she drove at 70MPH and 50MPH be x and y respectively.

x is one hour greater than y, so we have: x=y+1··· (1)

The distances she drove at 70MPH and 50 MPH are 70x and 50y respectively, and the difference between them is 100 miles.   So, we have: 70x-50y=100 

Divide both sides by 10.   We have: 7x-5y=10 ··· (2)

Solve the equations for y substituting (1) into (2).   We have: 7(y+1)-5y=10

Remove the brackets and simplify the equation, getting 2y=3, so y=1.5 (hours)

Plug y=1.5 into (1).   We have: x=1.5+1=2.5 (hours)

CK: Plug x=2.5 and y=1.5 into the left side of (2): 7(2.5)-5(1.5)=10, so LHS=RHS   CKD.

The answer: She drove 2.5 hours at 70MPH, then 1.5 hours at 50 MPH.