Question

Two planes leave from Atlanta, Georgia. One makes a 7.4 hr flight to Seattle, Washington, and the other makes a 2.6 hr flight to Boston, Massachusetts. The plane to Boston averages 60 mph slower than the plane to Seattle. If the total distance traveled by both planes is ,3124 determine the average speed of each plane.

Answer 1

To find the average speeds of both planes, we set up an equation using the distance formula and solved for the Seattle plane's speed. The Seattle plane's speed is calculated to be 328 mph, and by subtracting 60 mph, we found the Boston plane's speed to be 268 mph.

Step-by-step explanation:

Let's denote the average speed of the plane to Seattle as s mph. According to the problem, the plane to Boston flies at a speed of (s - 60) mph. We are given that the plane to Seattle flies for 7.4 hours and the plane to Boston for 2.6 hours. The total distance both planes travel together is 3124 miles.

The distance traveled can be determined by the formula: distance = speed × time. Therefore, the distance for the Seattle plane is 7.4s, and for the Boston plane, it is 2.6(s - 60). Adding these distances gives us the total distance:

7.4s + 2.6(s - 60) = 3124 miles

Now, we solve for s:

1. 7.4s + 2.6s - 156 = 3124
2. Combine like terms: 10s - 156 = 3124
3. Add 156 to both sides: 10s = 3280
4. Divide both sides by 10: s = 328

Thus, the average speed of the plane to Seattle is 328 mph, and the average speed of the plane to Boston is 268 mph (328 mph - 60 mph).

Answer 2

Given:

Two planes leave from Atlanta, Georgia.

One makes a 7.4 hours flight to Seattle, Washington and the other makes a 2.6 hours flight to Boston, Massachusetts.

The plane to Boston averages 60 mph slower than the plane to Seattle.

The total distance traveled by both plan is 3125 mi.

Required:

We need to find the Average speed of each plane

Step-by-step explanation:

Speed of Seattle plane is S

Speed of Boston plane is B

by The plane to Boston averages 60 mph slower than the plane to Seattle

we can say that

`B=S-60`

Formula of distance is the rate of speed times time

`d=rt`

Where d is distance

r is rate of speed

t it time

Now total distance traveled by both plane is 3124 mi

so

`3124=7.4S+2.6B`

substitute the value of B

`\begin{gathered} 3124=7.4S+2.6(S-60) \\ 3124=7.4S+2.6S-156 \\ 3280=10S \\ 328=S \end{gathered}`

Now to find B

`\begin{gathered} B=S-60 \\ B=328-60 \\ B=268 \end{gathered}`

Final answer:

Average speed of S is 328 mph

Average speed of B is 268 mph