A boy started on a trip across a lake by a motorboat After h

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 ?

Solution

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