Question

The Goodyear blimp flies 153 miles with a tailwind (with the wind) in the same time it travels 57 miles with a headwind (against the wind). If the speed of the wind is 16 mph, what is the speed of the blimp in still air?

Answer 1

Using the relation between velocity, distance and time, it is found that the speed of the blimp in still air is of 35 mph.

What is the relation between velocity, distance and time?

Velocity is distance divided by time, that is:

$v = \frac{d}{t}$

153 miles with a tailwind (with the wind), that is, with a velocity of v + 16, so:

$v + 16 = \frac{153}{t}$

$(v + 16)t = 153$

$t = \frac{153}{v + 16}$

57 miles with a headwind (against the wind), that is, with a velocity of v - 16, hence:

$v - 16 = \frac{57}{t}$

$(v - 16)t = 57$

$t = \frac{57}{v - 16}$

Since the times are equal, we have that:

$\frac{153}{v + 16} = \frac{57}{v - 16}$

153(v - 16) = 57(v + 16)

96v = 3360

v = 3360/96

v = 35.

The speed of the blimp in still air is of 35 mph.

More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569