Question

jocelyn recently flew to visit her grandchildren who live 1200 miles away, and she spent a total of 10 hours on the airplane for the round trip. if the airplanes speed was 250 miles per hour, what was the speed of the jet stream?

a. 50 miles per hour
b. 70 miles per hour
c. 80 miles per hour
d. 45 miles per hour

Explanation:

Step1: Define variables

Let \(x\) = speed of jet stream (mph).
One-way distance = 1200 miles.
Ground speed with jet stream: \(250 + x\) mph.
Ground speed against jet stream: \(250 - x\) mph.

Step2: Set up time equation

Total time = time with stream + time against stream.
Time = \(\frac{\text{distance}}{\text{speed}}\), so:
$$\frac{1200}{250 + x} + \frac{1200}{250 - x} = 10$$

Step3: Simplify the equation

Multiply all terms by \((250+x)(250-x)\):
$$1200(250 - x) + 1200(250 + x) = 10(250+x)(250-x)$$
Expand left side:
$$1200(250 - x + 250 + x) = 1200 \times 500 = 600000$$
Expand right side using \(a^2 - b^2\):
$$10(250^2 - x^2) = 10(62500 - x^2) = 625000 - 10x^2$$

Step4: Solve for \(x\)

Set equal and rearrange:
$$600000 = 625000 - 10x^2$$
$$10x^2 = 625000 - 600000 = 25000$$
$$x^2 = 2500$$
$$x = 50$$ (speed is positive)

Answer:

A. 50 miles per hour