A boat can travel 10 miles against a current in the same time that it can travel 40 miles with the current. The rate of the current is 3 mph. Find the rate of the boat in still water.

x = 5 mph

the rate of the boat in still water is 5 mph.

Step-by-step explanation:

Let x represent the speed of the boat in still water;

Given that the rate of the current is 3 mph.

When it is traveling against current, its relative speed is;

v1 = x - 3

When it is traveling with current, its relative speed is;

v1 = x + 3

Given;

A boat can travel 10 miles against a current in the same time that it can travel 40 miles with the current.

d1 = 10 miles

d2 = 40 miles

Distance = speed × time

time = distance/speed

The time taken for both cases are the same t;

t = d1/v1 = d2/v2

d1/v1 = d2/v2

Substituting the values;

10/(x-3) = 40/(x+3)

Cross multiply;

10(x+3)= 40(x-3)

10x + 30 = 40x - 120

Collecting the like terms;

40x -10x = 120+30

30x = 150

x = 150/30

x = 5 mph

the rate of the boat in still water is 5 mph.

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.