Question

An airplane travels 460 miles from San Diego to San Francisco in 2.5 hours, going against the wind. The return trip is with the wind, and takes only 2 hours. Find the rate of the airplane with no wind. Find the rate of the wind.

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Answer 1

To find the rate of the airplane with no wind and the rate of the wind, you can use a system of equations based on the given information. By solving these equations, you can find the desired rates.

Step-by-step explanation:

To find the rate of the airplane with no wind, we can use the formula:

Rate of airplane with wind - Rate of wind = Rate of airplane with no wind

Let's say the rate of the airplane with wind is A mph and the rate of the wind is W mph. Based on the given information:

A - W = Rate of airplane with no wind

For the trip from San Diego to San Francisco:

460 miles = (A - W) * 2.5 hours

And for the return trip from San Francisco to San Diego:

460 miles = (A + W) * 2 hours

By solving these two equations, you can find A and W. A will give you the rate of the airplane with no wind, and W will give you the rate of the wind.

Answer 2

distance=rate times time
distance=460
rate-wind=rate against wind
rate+wind=rate with wind
2.5=time aginst wind
2=time with wind
so
460=(rate-wind) times 2.5
and
460=(rate+wind) times 2

solve for rate
460=(rate-wind) times 2.5
divide both sides by 2.5
184=rate-wind

460=(rate+wind) times 2
divide by 2
230=rate+wind

we have
184=rate-wind
230=rate+wind
add them

184=rate-wind
230=rate+wind +
414=2rate+0wind
414=2rate
divide by 2
207=rate

answer is 207 miles per hour