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mattiewal · Mar 21, 2009, 12:23 PM

Solving a word problem using a system of linear equations:
A motorboat travels in 456kkm/8 hr hours going upstream and in 534 km in 6 hours going downstream. What is the speed of the boat in still water, and what is the speed of the current?

galactus · Mar 21, 2009, 01:03 PM

Let $r_{b}$ =the speed of the boat and $r_{c}$ equal the speed of the current.

Since d=rt.

When the boat is going upstream it is going against the current, so the rate is

$r_{b}-r_{c}$

Going downstream it is $r_{b}+r_{c}$

$534=6(r_{b}+r_{c})$

$456=8(r_{b}-r_{c})$

Solve for the two rates.

sarnian · Mar 22, 2009, 04:57 AM

Hello mattiewal

Call the real speed of boat a, call speed of water current b.
Total distance travelled = travel speed times time.
The travel speed is real boat speed + or - speed of current.

456 = 8(a - b) --> 456/8 = .a - b --> 57 = a - b
534 = 6(a + b) --> 534/6 = a + b --> 89 = a + b

Add together to eliminate b and solve a (real boat speed). Than solve b (current speed).
Note that both a and b are in Km/hr.

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MARICELA125 · May 11, 2010, 06:33 PM

A local hamburger shop sold a combined total of hamburgers and cheeseburgers on Sunday. There were fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Sunday?

MARICELA125 · May 11, 2010, 06:34 PM

A local hamburger shop sold a combined total of hamburgers and cheeseburgers on Sunday. There were fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Sunday?