Question

Problem
At full speed, Hal travels 600 miles in 2 hours
with the wind. The same distance against
the wind takes 3 hours.
What's the maximum speed of Hal's airplane
in still air? What's the speed of the wind?​

Answer 1

Answer:

The maximum speed of Hal's airplane in still air is:

$v= 250\ miles/h$

The speed of the wind

$c = 50\ miles/h$

Step-by-step explanation:

Remember that the velocity v equals the distance d between time t.

$v=\frac{d}{t}$  and $t*v=d$

The distance that Hal travels when traveling with the wind is:

$(2\ hours)(v + c) = 600$ miles

Where v is the speed of Hal and c is the wind speed.

The distance when traveling against the wind is:

$(3\ hours)(v-c) = 600$ miles

Now we solve the first equation for v

$(2)(v + c) = 600$

$2v + 2c = 600$

$2v= 600-2c$

$v= 300-c$

Now we substitute the value of v in the second equation and solve for c

$3((300-c)-c) = 600$

$3(300-2c) = 600$

$900-6c = 600$

$-6c = 600-900$

$-6c = -300$

$6c = 300$

$c = 50\ miles/h$

Then:

$v= 300-(50)$

$v= 250\ miles/h$

The maximum speed of Hal's airplane in still air is:

$v= 250\ miles/h$

The speed of the wind

$c = 50\ miles/h$