Rowing Distance Calculation

This solution determines the distance to a place based on rowing speeds and time taken for a round trip.

Key Information Extraction

• Speed in still water (Ashok's speed), $v_s = 43.5$ kmph.
• Speed of the river current, $v_r = 14.5$ kmph.
• Total time for the round trip (to the place and back), $T = 90$ minutes.

Speeds Calculation

The speed of the boat changes depending on whether it travels downstream (with the current) or upstream (against the current).

• Downstream Speed ($v_d$): Speed in still water plus the river speed. $v_d = v_s + v_r = 43.5 + 14.5 = 58$ kmph.
• Upstream Speed ($v_u$): Speed in still water minus the river speed. $v_u = v_s - v_r = 43.5 - 14.5 = 29$ kmph.

Round Trip Time

Convert the total time from minutes to hours for consistency with speed units (kmph).

• Total time $T = 90$ minutes $= \frac{90}{60}$ hours $= 1.5$ hours.

Distance Calculation

Let $d$ be the distance to the place from the starting point (one way).

The time taken to travel downstream is $t_d = \frac{d}{v_d}$ and the time taken to travel upstream is $t_u = \frac{d}{v_u}$.

The total time is the sum of the time taken for both legs of the journey:

$T = t_d + t_u$

$1.5 = \frac{d}{58} + \frac{d}{29}$

To solve for $d$, find a common denominator:

$1.5 = \frac{d}{58} + \frac{2d}{58}$

$1.5 = \frac{d + 2d}{58}$

$1.5 = \frac{3d}{58}$

Now, isolate $d$:

$3d = 1.5 \times 58$

$3d = 87$

$d = \frac{87}{3}$

$d = 29$

Therefore, the place is 29 km from the starting point.