Question 64946: A boy started on a trip across a lake by a motorboat. After he had travelled 15 km, the motor failed and he had to use a banca for the remaining 6 km to his destination. His average speed by motor was 4 kph faster than his average speed while rowing a banca. If the entire trip took five and a half hours, what was his average speed while rowing ?
dear tuitor ,
ihave been trying this problem too many times but cant. This what i get
d = rt
motorboat d= 15 km r= r+4 t = t
banca d= 6 km r= r t= 5.5 - t
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! You have definitely got the right formula so that's a big plus. The way I worked it, we end up with a quadratic equation which makes it a little more complicated than most word problems. Maybe another tutor will find an easier way.
As you suggest, we'll use the formula: d=rt or t=d/r
Let r=average speed in banca
Average speed by motor, we are told, is r+4
Now we know that the time spent in the banca (6/r) plus the time spent in the motorboat (15/(r+4)) equals 5.5 hours so our equation to solve is:
(6/r)+15/(r+4)=5.5 multiply both sides by(r)(r+4) to get rid of the fractions and r's in the denominator:
((r)(r+4))(6/r)+(15(r)(r+4))/(r+4)=5.5(r)(r+4) simplifying we get:
6(r+4)+15r=5.5r^2+22r further simplifying:
6r+24+15r=5.5r^2+22r which gives:
5.5r^2+22r-21r-24=0
5.5r^2+r-24=0 Now we'll solve this using the quadratic formula:
r=(-1+or-sqrt(1+528))/11
r=(-1+or-(23))/11
r=+22/11 or
r=2mph rowing speed
r also has a negative value which we will discount
r+4=2+4= 6mph speed of the boat
ck
6/2+15/6=5.5
3+2.5=5.5
5.5=5.5
Hope this helps. Happy holidays-----ptaylor
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