Q. 300 Stu trained for 3 hoursyesterday... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 300 (page 718)

Stu trained for 3 hours
yesterday. He ran 14 miles and
then biked 40 miles. His biking
speed is 6 mph faster than his
running speed. What is his
running speed?

Short Answer

Expert verified

The running speed of stu is $14 m p h$

Step by step solution

Given information

We are given that the biking

speed is 6 mph faster than his

running speed. Stu trained for 3 hours.

We draw a diagram to help us visualize

The diagram can be given as

Write an equation for her running speed and biking speed

Let the running speed of Stu be $r$ .

And the biking speed is $6 m p h$ faster than running speed

Hence the biking speed of Stu be $r + 6$

Step 4: The distances are given, enter them into the chart. Since D=rt, we solve for t and get t=Dr. We divide the distance by the rate in each row, and place theexpression in the time column.

We write the chart.

	Rate	Time	Distance
Running	$r$	$\frac{14}{r}$	$14$
Biking	$r + 6$	$\frac{40}{r + 6}$	50

Write the word sentence and translate it into the math equation

The word sentence can be given as

Her Running time plus biking time is $3 h r s$

The math equation can be given as

$\frac{14}{r} + \frac{40}{r + 6} = 3$

Simplify and solve

We get

$\frac{14}{r} + \frac{40}{r + 6} = 3 14 (r + 6) + 40 r = 3 r (r + 6) 14 r + 84 + 40 r = 3 r^{2} + 18 r 3 r^{2} - 36 r - 84 = 0 r^{2} - 12 r - 28 = 0$

Further factoring we get

$r^{2} - 14 r + 2 r - 28 = 0 r (r - 14) + 2 (r - 14) = 0 (r - 14) (r + 2) = 0$

Therefore either $r = 14$ or $r = - 2$

As the speed cannot be negative hence the speed is role="math" localid="1645071134688" $14 m p h$

Conclusion

The running speed of Stu is $14 m p h$

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91影视

Stu trained for 3 hours
yesterday. He ran 14 miles and
then biked 40 miles. His biking
speed is 6 mph faster than his
running speed. What is his
running speed?

Short Answer

Step by step solution

Given information

We draw a diagram to help us visualize

Write an equation for her running speed and biking speed

Step 4: The distances are given, enter them into the chart. Since D=rt, we solve for t and get t=Dr. We divide the distance by the rate in each row, and place theexpression in the time column.

Write the word sentence and translate it into the math equation

Simplify and solve

Conclusion

One App. One Place for Learning.

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91影视

Stu trained for 3 hoursyesterday. He ran 14 miles andthen biked 40 miles. His bikingspeed is 6 mph faster than hisrunning speed. What is hisrunning speed?

Short Answer

Step by step solution

Given information

We draw a diagram to help us visualize

Write an equation for her running speed and biking speed

Step 4: The distances are given, enter them into the chart. Since D=rt, we solve for t and get t=Dr. We divide the distance by the rate in each row, and place theexpression in the time column.

Write the word sentence and translate it into the math equation

Simplify and solve

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Calculus

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Stu trained for 3 hours
yesterday. He ran 14 miles and
then biked 40 miles. His biking
speed is 6 mph faster than his
running speed. What is his
running speed?