Question 809427: Two boats leave from the same point at the same time. One boat travels due east and the other travels due
north. One boat travels 6 kilometers faster than the other. After 4 hours, the boats are 67 kilometers apart.
a. Let x be the speed of the slower boat. Write a quadratic equation that models the
situation.
b. What are the solutions, to the nearest hundredth?
c. What are the speeds of the boats? Round your answers to the nearest hundredth.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Two boats leave from the same point at the same time.
One boat travels due east and the other travels due north.
One boat travels 6 kilometers faster than the other.
After 4 hours, the boats are 67 kilometers apart.
:
a. Let x be the speed of the slower boat.
then
(x+6) = speed of the faster boat
then
4x = distance traveled by the slow boat after 4 hrs
and
4(x+6) = (4x+24) = distance traveled by the faster boat
:
Write a quadratic equation that models the situation.
Using pythag
(4x)^2 + (4x+24)^2 = 67^2
16x^2 + 16x^2 + 192x + 576 = 4489
32x^2 + 192x + 576 - 4489 = 0
32x^2 + 192x - 3913 = 0
use the quadratic equation, after a lot of tedious math, I got:
x = +8.458 and -14.458
:
b. What are the solutions, to the nearest hundredth?
8.46 and -14.46
:
c. What are the speeds of the boats? Round your answers to the nearest hundredth.
Slow boat: 8.46 mph, fast boat 14.46 mph
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