Question

In his boat, Sheldon can travel 45 mi downstream in the same time that it takes to travel 9 mi upstream. If the rate of the current is 6 mph, find the rate of the boat in

still water.

Answer 1

The rate of the boat in still water is 9 mph.

Step-by-step explanation:

To find the rate of the boat in still water, we need to use the formula:

rate of boat in still water = (rate downstream + rate upstream) / 2

Given that the rate of the current is 6 mph, we can determine the rate downstream and rate upstream:

rate downstream = rate of boat in still water + rate of current = x + 6 mph

rate upstream = rate of boat in still water - rate of current = x - 6 mph

Since Sheldon can travel 45 mi downstream in the same time it takes to travel 9 mi upstream, we can set up the equation:

45 / (x + 6) = 9 / (x - 6)

Cross multiplying and simplifying the equation gives:

45(x - 6) = 9(x + 6)

45x - 270 = 9x + 54

36x = 324

x = 9 mph

So, the rate of the boat in still water is 9 mph.

Answer 2

9 mph

Step-by-step explanation:

-let x be the speed of current and t be time. The speed equation for both directions can then be represented as:

`Speed=(Distance)/(Time)\\\\\#Upstream\\(u-6)t=9\\\\\#Donwstream\\\\(u+6)t=45`

#Since t is equal in both, we can do away with t.

#We the divide the downstream equation by the upstream equation as:

`(u+6)/(u-6)=(45)/(9)\\\\(u+6)=5(u-6)\\\\u+6=5u-30\\\\4u=36\\\\u=9`

Hence, the boat's speed in still water is 9 mph