The upstream speed of a boat is 15 km/hr and the ratio of time taken by the boat to cover 105 km upstream and 108 km downstream 7 : 6 respectively. Find the speed of stream (in km/hr)?

Speed of boat upstream = 15 km/hr

Distance upstream = 105 km

Distance downstream = 108 km

Ratio of time taken upstream : downstream = 7 : 6

We need to find: Speed of stream (km/hr)

Let:

Speed of boat in still water = b km/hr

Speed of stream = s km/hr

Then:

Upstream speed = b - s
Downstream speed = b + s

Time = Distance / Speed

Given ratio of times:

​$$\frac{\dfrac{105}{b - s}}{\dfrac{108}{b + s}} = \frac{7}{6}$$​​

Also, b – s = 15

Substitute b – s = 15 into the time ratio:

​$$\frac{\dfrac{105}{15}}{\dfrac{108}{b + s}} = \frac{7}{6}$$​​

​$$\frac{105 \times (b + s)}{15 \times 108} = \frac{7}{6}$$

​

$$\frac{7(b + s)}{108} = \frac{7}{6}$$

​
$$\frac{b + s}{108} = \frac{1}{6}$$​​
b + s = 18
b + s = 18
b – s = 15

Add both equations:

2b = 33 => b = 16.5

Substitute b = 16.5 into b – s = 15

16.5 – s = 15 => s = 1.5

Speed of stream = 1.5 km/hr