If The Speed Of The Current Was 2 Mph, What Was The Speed Of The Boat?
A boat took 12 miles longer to travel 3 miles upstream than to travel the same distance downstream.
A. 6 mph
B. 8 mph
C. 10 mph
D. 11 mph
E. 7 mph
Answer:
Let "b" = the speed of the boat, and "c" = the speed of the current.
3/(b-c) = 12/60 + 3/(b+c), assuming the difference in time is 12 minutes.
This equation can be expressed over a common denominator of b2-c2:
3(b+c)/(b2-c2) = (1/5)(b2-c2)/(b2-c2) + 3(b-c)/(b2-c2)
15b + 15c = b2-c2 + 15b - 15c (multiply both sides by 5(b2-c2), expand the numerator)
b2 = c2 + 30c (add c2+15c to both sides)
b = √(c(c+30)) = √(2(32)) = √64 = 8 (take square root, substitute numbers for the speed of the current)
The speed of the boat be 8 mph.
Resolved Questions:
I Need To Know The Square Meter Of Length 1.5meter By Width 1meter...
Square meter means area and judging from the values given the shape is a rectangle We are given L=1.5 W=1 the formula for the nouns of a rectangle is A=LxW So A=1.5x1 Multiplying A=1.5
I Would Like To Get Printable Monthly Calendar Pages That Fit On An...
For free online calendars try http://incompetech.com/beta/cal-monthly/ At one time, I got a monthly calendar for 2009 that I could easily access on msn window xp. I had that on Vista Windows, but uninstalled them and so went my calendars. I would...
Does Not Having Recess In Middle School Cause Stress?
Recess gives students the opportunity to: Play Eat/drink Have fun Without recess students would be: cranky have a monotonous year be bored with what they are studying Which all would add up to do stress. Therefore recess is important to...
Answer:
Let "b" = the speed of the boat, and "c" = the speed of the current.
3/(b-c) = 12/60 + 3/(b+c), assuming the difference in time is 12 minutes.
This equation can be expressed over a common denominator of b2-c2:
3(b+c)/(b2-c2) = (1/5)(b2-c2)/(b2-c2) + 3(b-c)/(b2-c2)
15b + 15c = b2-c2 + 15b - 15c (multiply both sides by 5(b2-c2), expand the numerator)
b2 = c2 + 30c (add c2+15c to both sides)
b = √(c(c+30)) = √(2(32)) = √64 = 8 (take square root, substitute numbers for the speed of the current)
The speed of the boat be 8 mph.
Resolved Questions:
I Need To Know The Square Meter Of Length 1.5meter By Width 1meter...
Square meter means area and judging from the values given the shape is a rectangle We are given L=1.5 W=1 the formula for the nouns of a rectangle is A=LxW So A=1.5x1 Multiplying A=1.5
I Would Like To Get Printable Monthly Calendar Pages That Fit On An...
For free online calendars try http://incompetech.com/beta/cal-monthly/ At one time, I got a monthly calendar for 2009 that I could easily access on msn window xp. I had that on Vista Windows, but uninstalled them and so went my calendars. I would...
Does Not Having Recess In Middle School Cause Stress?
Recess gives students the opportunity to: Play Eat/drink Have fun Without recess students would be: cranky have a monotonous year be bored with what they are studying Which all would add up to do stress. Therefore recess is important to...