Question

Two cars start moving from the same point. The first car travels north at 80 mi/hr. and the second travels east at 88 ft/sec. How far apart, in miles, are the two cars two hours later?

Answer 1

Two hours later the two cars will be 200 miles apart.

Explanation:

First let's convert 88 ft/sec into miles/hour

`(88"ft")/(1" sec")" x "(3600" sec")/(1 " hour")" x "(1" mile" )/(5280" ft") = 60" miles/hour"`

Now we have 1 car going North at 80 mi/h and another going East at 60 mi/h. These two directions have a `90^o` angle between them, so each car will be making a side of a right triangle. After two hours the car going North will have driven for 160 miles and the one going East driven for 120 miles. The distance between these two cars is the hypotenuse of the triangle with those two sides, and we know from Pythagoras' Theorem that:

`A^2+B^2=C^2` so:

`160^2+120^2=C^2`
`C^2=25600+14400`
`C^2=40000`
`C=sqrt(40000)`
`color(blue)(C=200)`