SOLUTION: a motorboat travels 9 mph in still water. It takes 5 hours longer to travel 55 miles going upstream than it does going downstream. Find the rate of the current. Hint (x+9) is goin
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Question 813725: a motorboat travels 9 mph in still water. It takes 5 hours longer to travel 55 miles going upstream than it does going downstream. Find the rate of the current. Hint (x+9) is going downstream and (x-9) is going upstream. round to nearest tenth.
Found 3 solutions by mananth, josgarithmetic, MathTherapy:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
still water 9 mph
current - x mph
down stream = 9+x
upstream = 9-x
time upstream - time downstream = 5 hours
t=d/r
55/(9-x) -55/(9+x)=5
55(9+x)-55(9-x)=5(9^2-x^2)
495+55x-495+55x=405-5x^2
5x^2+110x-405=0
Find the roots of the equation by quadratic formula
a= 5 , b= 110 , c= -405
b^2-4ac= 12100 + 8100
b^2-4ac= 20200
x1=( -110 + 142.13 )/ 10
x1= 3.21
x2=( -110 -142.13 ) / 10
x2= -25.21
Ignore negative value
current speed 3.2 mph
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Direction__________speed____________time________________distance
UPstream___________x-9______________y+5_________________55
DOWNstream_________x+9______________y___________________55
x is as you have assigned, the speed of the boat in still water.
y is the time in hours to travel downstream the 55 miles.
Basic idea is Rate*Time=Distance. This gives two equations:
and , neither linear.
and .
If we have one more equation, this might be easier. Trying to equate the distances,
Continue solving this for x (or y if someone wants):
Try substituting this into the simplified downstream equation:
multiply both sides by 25,
General Solution to Quadratic Equation:
279625=25*5*2237
HOURS
This means that y+5 to go upstream was 7.88 hours.
Remember in this analysis, we found, ?
Now we can calculate the boat's speed in still water.
miles per hour.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
a motorboat travels 9 mph in still water. It takes 5 hours longer to travel 55 miles going upstream than it does going downstream. Find the rate of the current. Hint (x+9) is going downstream and (x-9) is going upstream. round to nearest tenth.
Speed of current: 3.21267 ≈ mph
You can do the check!!
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