Q 431. A boat travels 140 miles downstr... [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 431. (page 1008)

A boat travels 140 miles downstream in the same time as it travels 92 miles upstream. The speed of the current is 6 mph. What is the speed of the boat?

Short Answer

Expert verified

The speed of the boat is 29 mph.

Step by step solution

Step 1. Given information.

A boat travels 140 miles downstream in the same time as it travels 92 miles upstream.

The speed of the current is 6 mph.

Let's take $r =$ the speed of the boat. then,

The speed of the boat increases when it travels downstream and the speed becomes $r + 6$ .

The speed of the boat decreases when it travels upstream and the speed becomes $r - 6$ .

Step 2. Find the speed of the boat.

Organize the given information in a chart:

	Rate	Time $(t) = \frac{D}{r}$	Distance $D = r 路 t$
Downstream	$r + 6$	$\frac{140}{r + 6}$	$140$
Upstream	$r - 6$	$\frac{92}{r - 6}$	$92$

Since the times are equal, equate the times in both cases,

$\frac{140}{r + 6} = \frac{92}{r - 6}$

Multiply both sides by the LCD,

$(r + 6) (r - 6) (\frac{140}{r + 6}) = (r + 6) (r - 6) (\frac{92}{r - 6})$

Simplify,

$140 (r - 6) = 92 (r + 6) 140 r - 840 = 92 r + 552 140 r - 92 r = 552 + 840 48 r = 1392 r = 29$

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91影视

A boat travels 140 miles downstream in the same time as it travels 92 miles upstream. The speed of the current is 6 mph. What is the speed of the boat?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the speed of the boat.

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