A man makes a trip in 3T hours. Two thirds of the distance travelled was by car and the remainder by boat. If his rate by car was three times his rate by boat, then the number of hours spent in the boat was:

(A) 6/5 T
(B) T
(C) 3/4 T
(D) 9/5 T

I'm confused and don't know how to start this problem. Could someone please explain to me how to get the answer?

2. Originally Posted by xwrathbringerx
A man makes a trip in 3T hours. Two thirds of the distance travelled was by car and the remainder by boat. If his rate by car was three times his rate by boat, then the number of hours spent in the boat was:

(A) 6/5 T
(B) T
(C) 3/4 T
(D) 9/5 T

I'm confused and don't know how to start this problem. Could someone please explain to me how to get the answer?
Let speed of boat be v. Then speed of car = 3v.

Let total distance be D. Then distance travelled by car = 2D/3 and distance travelled by boat = D/3.

Time = (distance)/(speed). Therefore:

$\displaystyle t_{\text{car}} = \frac{2D/3}{3v} = \frac{2D}{9v}$.

$\displaystyle t_{\text{boat}} = \frac{D/3}{v} = \frac{D}{3v} = \frac{3D}{9v}$.

Therefore:

$\displaystyle 3T = t_{\text{car}} + t_{\text{boat}} = \frac{5D}{9v}$

$\displaystyle \Rightarrow D = \frac{27vT}{5}$.

Therefore:

$\displaystyle t_{\text{boat}} = \frac{3D}{9v} = \frac{81vT}{45v} = \frac{81}{45} \, T = \frac{9}{5} \, T$.