Question

A boat heads south at 1,200 mph while a steamer heads east at 500 mph. If they started from the same dock and at the same time, when will the distance between them be 1,300 mi?

Answer 1

Answer: After t=1 hour the distance between the boat and the steamer be 1300 mi.

Explanation:

Given the speed of boat = 1200 mph

the speed of steamer =500 mph

Distance traveled by boat in time "t"=
`(distance)/(time)=(1200)/(t)`

Distance traveled by steamer in time time "t"=
`(500)/(t)`

As boat head south and steamer heads east ∴ they will make a right angle triangle with hypotenuse=shortest distance between them =1300mi(given)

By Pythagoras theorem

`(Perpendicular)^2+(Base)^2=(Hypotenuse)^2\\\\\Rightarrow((1200)/(t))^2+((500)/(t))^2=(1300)^2\\\\\Rightarrow(1440000)/(t^2)+(250000)/(t^2)=1690000\\\\\Rightarrow(1690000)/(t^2)=1690000\\\\\Rightarrow\ t^2=(1690000)/(1690000)=1`

⇒t=1 hour

Thus, after t= 1 hour the distance between them be 1300 mi.

Answer 2

If they started at a same time the distance between them will be 1300 mi exactly after an hour (1 hour).

(1200 m/h)^2 + (500 m/h)^2 = (1300 m)^2

Time is 1 Hour

So the distance between the boat heads and steamer heads if they started the same time and be 1300 mi is 1 hour.