Q 599. John can ride his bike 8聽mph fa... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q 599. (page 1027)

John can ride his bike $8$ mph faster than Luke can ride his bike .It takes Luke $3$ hour longer than John to ride $48$ miles. How fast can John ride his bike?

Short Answer

Expert verified

Speed of John is $16$ mph.

Step by step solution

Step 1. Given information.

John can go $8$ mph faster than Luke. If it takes Luke $3$ hours longer than John to go $48$ miles.

Let the speed of Luke $= r$

Let the speed of John $r + 8$

Step 2. To find the time taken.

Organize the given information in a chart:

	Rate	Time $t = \frac{d}{r}$	Distance $d = t 路 r$
Luke	$r$	$\frac{48}{r}$	$48$
John	$r + 8$	$\frac{48}{r + 8}$	$48$

Time taken by Luke is $3$ hour longer than John.

Time taken by Luke $-$ Time taken by John $= 3$

localid="1657244022553" $\frac{48}{r} - \frac{48}{r + 8} = 3$

Multiply both sides by the LCD $= r (r + 8)$ .

$r (r + 8) \frac{48}{r} - r (r + 8) \frac{48}{r + 8} = 3 r (r + 8) (r + 8) 路 48 - 48 r = 3 r^{2} + 24 r 48 r + 384 - 48 r = 3 r^{2} + 24 r 3 r^{2} + 24 r - 384 = 0 r^{2} + 8 r - 128 = 0 r = 8, - 16$

So speed can not negative.

Therefore $r = 8$

Now speed of John = $r + 8 = 8 + 8 = 16 m p h$

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91影视

John can ride his bike $8$ mph faster than Luke can ride his bike .It takes Luke $3$ hour longer than John to ride $48$ miles. How fast can John ride his bike?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. To find the time taken.

One App. One Place for Learning.

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91影视

John can ride his bike 8mph faster than Luke can ride his bike .It takes Luke 3hour longer than John to ride 48miles. How fast can John ride his bike?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. To find the time taken.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Decision Maths

Discrete Mathematics

Statistics

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

John can ride his bike $8$ mph faster than Luke can ride his bike .It takes Luke $3$ hour longer than John to ride $48$ miles. How fast can John ride his bike?