Write an equation and graph an equation that shows the numbers of minutes the sailboat can use its sails and its motor to get to the island.
The owner of a sailboat takes passengers to an island 5 miles away to go snorkeling. A sailboat averages about 9 miles per hour when using its sails and about 14 miles per hour when using its motor.
You are looking for two times: Ts, the time that the boat uses sails, and Tm, the time that the boat uses its motor.
If the boat uses its sails for Ts hrs, how far did it go? Ts hours x 9 mi/hr = 9*Ts miles.
Similarly, Tm * 14 mi/hr = 14*Tm miles.
Add the two together to get the distance traveled using the sails Ts of the time and the motor Tm of the time:
D = 9Ts + 14Tm
We know that D = 5.
5 = 9Ts + 14Tm
Here want an answer in number minutes the time taken by the boat in using the boat by the sail and by the mototor.
The total distance covered is 5 miles.
The speed of the boat by sail = 9 mile/hour = 9/60 miles per minute.Let x be the distance covered by sail. Since time m1 taken for this is given by distance / speed per minute = x/(9/60) . Or
m1 = 60x/9 minutes.
m1 = 20x/3 minutes.
The distance covered by the motor of the sail = 5-x miles. The speed of the boat by motor = 14mile per hour = 14/60 miles per minute.
So the time m2 in minutes taken by the boat to cover (5-x) miles of distance = distance / speed per minute = (5-x)/(14/60)
m2 = (5-x)*60/14
m2 = 30(5-x)/7
Therefore the number of minutes the boat can use sail and motor are given by:
m1 = 20x/3...........(1) minutes and
m2 = 30(5-x)/7......(2) , where 0 < = x < = 5.
Therefore by eliminating x between eq(1) and (2), we get the single equation in m1 and m2 :
9*(1)*9 + 14*(2) eliminates x:
9m1 +14m2 = 60x+60(5-x)
9m1+14m2 = 60x+300-60x
9m1+14m2 = 300 is the required equation , where m1 and m2 are the speeds per minute of b sail and motor respectively.
How would you graph this? Can you put it into slope intercept form?