Question

A boat moves downstream at the rate of 1 km in 7.5 minutes and upstream at the rate of 5 km an hour . what is the speed (in km/hr) of the boat in the still water ?

Answer 1

downstream a = 1/(7.5/60) = 60/7.5 = 8 km/hr
upstream b = 5/1 = 5 km/hr

speed of the current = (a-b)/2 = (8-5)/2 = 3/2 = 1.5 km/hr

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Answer 2

Speed of boat in standing water is $\bold{6 \frac{1}{2} k m / h r}$

Solution:

The boat moves a distance of 1 km in 7.5 minutes, therefore the speed of the boat downstream is,  

The division between the distance and time covered by the boat $=\frac{\text {Distance boat travels downstream}}{\text {Time}}$

Now as to take out the time in hour,we divide 7.5 with 60.  

We use $\frac{7.5}{60}=\frac{1}{8} h o u r$.

Hence, the speed downstream is $=\frac{\text {Distance boat travels downstream}}{\text {Time}}$

$=\frac{1}{\frac{1}{8}}=8 k m / h r$

Now, speed upstream is 5 km/hr.

Therefore, the speed of still water = $\bold{\frac{1}{2}(\text {Speed of upstream}+\text { Speed of downstream)}}$ = $\bold{=\frac{1}{2}(8+5)=6 \frac{1}{2} k m / h r}$