Question

On a river, Q is the mid-point between two points P and R on the same bank of the river. A boat can go from P to Q and back in 12 hours, and from P to R in 16 hours 40 minutes. How long would it take to go from R to P ?

• A. $$3\frac{1}{3}hours$$
• B. 5 hours
• C. $$6\frac{2}{3}hours$$
• D. $$7\frac{1}{3}hours$$

Answer 1

Answer:

$$7\frac{1}{3}hours$$

Let PQ = QR = z km.

Let speed of boat in still water be x kmph. and speed of current be y kmph.

According to the question,

$\frac{z}{x+y}+\frac{z}{x-y}=12$ -------(1)

and $\frac{2z}{x-y}=16\frac{40}{60}$

$\frac{2z}{x-y}=16\frac{2}{3}=\frac{50}{3}$ --------(2)

By equation (1) × 2 – (2),

$\frac{2z}{x+y}+\frac{2z}{x-y}-\frac{2z}{x-y}=24-\frac{50}{3}$

$\frac{2z}{x+y}=\frac{72-50}{3}$

$=\frac{22}{3}=7\frac{1}{3}hours$