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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q.293 (page 716)

Chester rode his bike uphill 24 miles and then back downhill at 2 mph faster than his uphill. If it took him 2 hours longer to ride uphill than downhill, what was his uphill rate?

Short Answer

Expert verified

The uphill rate is 4 mph .

Step by step solution

01

Step 1. Given Information.

Chester rode his bike uphill 24 miles .

Downhill at 2 mph faster than his uphill .

It took him 2 hours longer to ride uphill than downhill .

02

. Equations for Ratio and Proportion

Let the uphill rate be x mph .

The formula for speed is as:-

$S p e e d = \frac{D i s \tan c e}{T i m e} T i m e = \frac{D i s \tan c e}{S p e e d}$

Time taken in uphill $= \frac{24}{x}$

Time taken in downhill $= \frac{24}{x + 2}$

Therefore, The equation is as:-

$\frac{24}{x} - \frac{24}{x + 2} = 2$

03

. Solving the Proportional equation .

Solving :-

$\frac{24}{x} - \frac{24}{x + 2} = 2 24 (x + 2) - 24 x = 2 x (x + 2) 24 x + 48 - 24 x = 2 x^{2} + 4 x 2 x^{2} + 4 x - 48 = 0$

Solving the quadratic equation , we get:-

$2 x^{2} + 4 x - 48 = 0 x^{2} + 2 x - 24 = 0 x^{2} + 6 x - 4 x - 24 = 0 x (x + 6) - 4 (x + 6) = 0 (x - 4) (x + 6) = 0 x = 4; x = - 6$

Since , The negative value of speed has no sense . Therefore, The uphill rate is 4 mph .

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