Question

Starting from the same place a plane took 1 hr longer to fly 705 mi to Atlanta, than to fly 470 mi to New Orleans. If the plane flew at the same rate for the entire trip, what was the flying time for the shorter leg? a. 1 2 hr c. 1 1 2 hrs b. 1hr d. 2 hrs

Answer 1

Answer: d. 2 hrs

Explanation:

Let x = Time taken(in hours) to fly 470 mi to New Orleans. (Shorter leg)

Then Time taken to fly 705 mi to Atlanta= x+1 (longer leg)

Since the plane flew at the same rate for the entire trip.

i.e. Speed 705 mi to Atlanta = Speed to fly to New orleans

`\Rightarrow\ (705)/(x+1)=(470)/(x)\ \ \ \ \ \ \ [\text{Speed}=\frac{\text{Distance}}{\text{Time}}]\\\\\Rightarrow\ 705x=470(x+1)\\\\\Rightarrow\ 705x=470x+470\\\\\Rightarrow\ 705x-470x=470 \\\\\Rightarrow\ 235x=470\\\\\Rightarrow\ x=(470)/(235) \\\\\Rightarrow\ x=2`

hence, the flying time for the shorter leg = 2 hours

So (d) is the correct option.