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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q.504. (page 1069)

Matheus can ride his bike for $30$ miles with the wind in the same amount of time that he can go $21$ miles against the wind. If the wind's speed is $6$ mph, what is Matheus' speed on his bike?

Short Answer

Expert verified

The speed is $34$ mph.

Step by step solution

01

Step 1. Given information.

Matheus can ride his bike for $30$ miles with the wind in the same amount of time that he can go $21$ miles against the wind.

If the wind's speed is $6$ mph.

02

Step 2. Find the equation for the given information.

Let $r$ is bike speed and $w$ is wind speed.

Rate with wind $= r + w$ and rate against wind $= r - w$ .

$30 = (r + 6) t 30 = r t + 6 t 鈰� 鈰� (1)$

$21 = (r - 6) t 21 = r t - 6 t 鈰� 鈰� (2)$

03

Step 3. Solve the equation.

$30 = r t + 6 t 21 = r t - 6 t \overset{炉}{51 = 2 r t} t = \frac{51}{2 r}$

Substitute the value of $t = \frac{51}{2 r}$ in the equation $30 = r t + 6 t$ .

localid="1663172768525" $30 = r 路 \frac{51}{2 r} + 6 路 \frac{51}{2 r} 30 = \frac{51}{2} + \frac{306}{2 r} 30 - \frac{51}{2} = \frac{306}{2 r} \frac{60 - 51}{2} = \frac{306}{2 r} \frac{9}{2} = \frac{306}{2 r} r = \frac{306 脳 2}{9 脳 2} r = 34$

04

Step 4. Simplified answer.

Hence, the speed of the bike is $34$ mph.

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