Question

The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return down stream to the original point in 4 hrs and 30 minutes. Find the speed of the stream:

• A. 4 km/hr
• B. 8 km/hr
• C. 4.5 km/hr
• D. 5 km/hr

Answer 1

Answer:

D. 5 km/hr

The speed of the stream is 5 km/hr.

Let the speed of the stream be $x$ km/hr.

* Speed Upstream: $(15 - x)$ km/hr

* Speed Downstream: $(15 + x)$ km/hr

* Total Time Taken: 4 hours 30 minutes = $4.5$ hours (or $\frac{9}{2}$ hours)

Using the formula $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$, we can set up the equation:

$\frac{30}{15 - x} + \frac{30}{15 + x} = 4.5$

1. Take the common denominator:

$30 \left( \frac{(15 + x) + (15 - x)}{(15 - x)(15 + x)} \right) = 4.5$

2. Simplify the numerator and apply the identity $(a-b)(a+b) = a^2 - b^2$:

$30 \left( \frac{30}{225 - x^2} \right) = 4.5$

$\frac{900}{225 - x^2} = 4.5$

3. Cross-multiply and solve for $x$:

$900 = 4.5 \times (225 - x^2)$

$900 = 1012.5 - 4.5x^2$

$4.5x^2 = 1012.5 - 900$

$4.5x^2 = 112.5$

$x^2 = \frac{112.5}{4.5} = 25$

$x = 5 \text{ km/hr}$