Mathematics, 28.12.2019 06:31 jaylennkatrina929

Aboat on a river travels downstream between two points, 20 mi apart, in one hour. the return trip against the current takes 2 1/ 2 hours (2hours and a half). what is the boat's speed (in still water)? b) how fast does the current in the river flow?

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Answer from: savidgarcia303

The speed of boat in still water is 14 miles per hour.

The speed of current is 6 miles per hour.

Step-by-step explanation:

Let v represent the speed of boat in still water and c represent speed of current.

We have been given that a boat on a river travels downstream between two points, 20 miles apart, in one hour.

The speed of boat downstream would speed of boat in still water plus speed of current that is (v+c) .

The return trip against the current takes 2 1/ 2 hours. The speed of boat against current would speed of boat in still water minus speed of current that is (v-c) .

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

Substituting our given values, we will get:

$v+c=\frac{20}{1}...(1)$

$v-c=\frac{20}{2.5}...(2)$

Adding both equations, we will get:

$v+c+(v-c)=\frac{20}{1}+\frac{20}{2.5}$

$v+c+v-c=\frac{20}{1}+\frac{20}{2.5}$

2v=20+8

2v=28

$\frac{2v}{2}=\frac{28}{2}$

v=14

Therefore, the speed of boat in still water is 14 miles per hour.

To find the speed of the current in the river, we will substitute v=14 in equation (1) as:

$14+c=\frac{20}{1}$

14+c=20

14-14+c=20-14

c=6

Therefore, the speed of current is 6 miles per hour.

Answer from: Quest

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200. after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes 1800 - 6400 which gets you 11,600.

Answer from: Quest

days of the week

step-by-step explanation:

javier earned more money then kyle, so that won't always be a constant term, but the days of the week do not change so that term is always constant.

edit: i meant

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