A boat, which moves at 12 miles per hour in water without a current, goes 45 miles upstream and 45 miles back again in 8 hours. Find the speed of the current to the nearest tent…

Question

asked Apr 17, 2021 180k views

1 Answer

MChan · Answer 1 · 2021-04-23T20:39:04+0000

Given:

Speed in still water = 12 miles per hour

Distance travel in upstream = 45 miles

Distance travel in downstream = 45 miles

Total time = 8 hours

To find:

The speed of current.

Solution:

Let the speed of current be x miles per hour.

Speed in upstream = (12-x) miles per hour

Speed in downstream = (12+x) miles per hour

We know that,

Time=(Distance )/(Speed)

Time to cover 45 miles in upstream =
(45)/(12-x)

Time to cover 45 miles in downstream =
(45)/(12+x)

Total time is 8 hours. So,

(45)/(12-x)+(45)/(12+x)=8

$45\left ((1)/(12-x)+(1)/(12+x)\right)=8$

Taking LCM, we get

$45\left ((12+x+12-x)/(12^2-x^2)\right)=8$

$45\left ((24)/(144-x^2)\right)=8$

(45* 24)/(8)=144-x^2

On further simplification, we get

45* 3=144-x^2

135=144-x^2

x^2=144-135

x^2=9

Taking square root on both sides.

$x=\pm √(9)$

$x=\pm 3$

Speed cannot be negative. So, x=3 only.

Therefore, the speed of the current is 3 miles per hour.