Chapter 4.CR, Problem 54CR

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

Chapter
Section

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

# Nasser rode his bicycle 66 miles in 4 1 2 hours. For the first 40 miles he averaged a certain rate, and then for the last 26 miles he reduced his rate by 3 miles per hour. Find his rate for the last 26 miles.

To determine

To Find:

The rate of Nasser for the last 26 miles.

Explanation

Formula used:

For the uniform-motion problems, the time taken by the moving object can be express as.

t=dv

Here, distance travelled is d, uniform rate or speed during travelling is v and time taken during travelling is t.

Calculation:

Consider the uniform rate during the first 40 miles is v then the rate during the last 26 miles becomes (vâˆ’3) miles per hour. Total time taken in travelling should be equal to the sum of the time taken to travel 40 miles and 26 miles respectively.

T=t1+t2â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰(1)

Here, the total time taken in travelling is T which is 412â€‰hours, the time is taken in 40 miles travelling is t1 and time taken in 26 miles is t2.

Substitute 412â€‰hours for T and the value of time taken in their respective distance in equation (1).

412â€‰=40v+26(vâˆ’3)

Multiply v(vâˆ’3) on both sides.

922v(vâˆ’3)=2v(vâˆ’3)(40v)+2v(vâˆ’3)[26(vâˆ’3)]9v2âˆ’27v=80vâˆ’240+52v9v2âˆ’159v+240=0

Re-arrange the terms.

3v2âˆ’53v+80=0â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰(2)

For the quadratic equation of the form av2+bv+v=0 the solutions are.

v1,2=âˆ’bÂ±b2âˆ’4ac2a

Comparing the general form of the quadratic equation with equation (2).

a=3,b=âˆ’53â€‰andâ€‰c=80

Therefore the rate of bicycles,

v1,â€‰2=âˆ’(âˆ’53)Â±(âˆ’53)2âˆ’4â‹…â€‰3â‹…â€‰802â‹…â€‰3

Take a positive sign for the first root value

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