Question

A motorboat maintained a constant speed of 12 miles per hour relative to the water in going 45 miles upstream and then returning. The total time for the trip was 8.0 hours. Use this information to find the speed of the current.

Answer 1

Answer: Speed of the current is 3 miles per hour.

Step-by-step explanation:

Since we have given that

Speed of motor boat = 12 miles per hour

Distance traveled upstream = 45 miles

Let the speed of the current be x

Total time taken by upstream and downstream = 8 hours

Relative speed for downstream is given by

$12+x$

Relative speed for upstream is given by

$12-x$

According to question, we have

$\frac{45}{12+x}+\frac{45}{12-x}=8\\\\\frac{45(12-x)+45(12+x)}{(12-x)(12+x)}=8\\\\\frac{45(12-x+12+x)}{144-x^2}=8\\\\\frac{24}{144-x^2}=\frac{8}{45}\\\\45\times 24=8(144-x^2)\\\\45\times 3=144-x^2\\\\135=144-x^2\\\\135-144=-x^2\\\\-9=-x^2\\\\x=\sqrt{9}=\pm3\\\\\text{But x=-3 will be igonored as speed cant be in negative}\\\\x=3\ mile\ per\ hour$

Hence, Speed of the current is 3 miles per hour.