You are leaving for a party at your cousin’s house in a city that is 150 km away. you will travel at an average rate of 50 km/hr. if you need to be at the party in 2.5 hours, how fast would you need to drive to get there?

If you travel at a constant rate, the equation which describes your traveling is

where s is the space traveled, v the velocity you're traveling at, and t is the time passed traveling.

You know the distance and the time, so let's solve the equation for speed:

So, if you plug the values, you have

So, you need to travel at an average speed of 60km/hr to be at the party in 2.5 hours. If you travel at an average speed of 50km/hr, you'll be there in three hours

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

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