I have a question dealing with the pythagorean theorem, and how to solve it?

Question

Greg drove at a constant speed in a rain storm for 220 miles. He took a break and the rain stopped. He then drove 208 miles at a speed that was 8mph faster than his previous speed. If he drove for 9 hours, find the car's speed for each part of the trip.

 

What was the rate of the car in the rain?

 

Please help me. I'm in college just trying to better myself. 

 

Answer 1

Hi Kourtney.

 

It looks like this questions doesn't deal with Pythagorean Theorem at all. It's safe to assume your driver drove in a straight line.

 

There are two parts to this question: one where he drives some constant speed, and one where he drives some constant speed plus 8.

 

Let's call his constant speed variable V.

 

He drove at speed V for 220 miles.

 

He drove at speed (V + 8) for 208 miles.

 

He drove for a total of 9 hours.

 

Now, you know that:

 

speed = distance/time

 

So

 

time = distance/speed

 

There are 2 different times to consider: the time for the first part of his trip, and the time for the second part of his trip.

 

time1 = distance1/speed1

 

time1 = 220/V

 

time2 = distance2/speed2

 

time2 = 208/(V+8)

 

time1 + time2 = 9 hours

 

So:

 

220/V + 208/(V+8) = 9

 

Time to do some algebra.

 

First find a common denominator for the left side.

 

(220*(V+8) + 208*V)/(V*(V+8)) = 9

 

Multiply both sides by V*(V+8)

 

220*(V+8) + 208*V = 9V*(V+8)

 

220V + 1760 + 208V = 9V^2 + 72V

 

Move everything to one side.

 

9V^2 - 356V - 1760 = 0

 

Now you have a quadratic equation to solve. Use any method you want. Quadratic formula is probably best.

 

V = 44, -4.45

 

You can't have a negative speed, so go ahead and cross out that solution.

 

V = 44 mph.

 

So he drove 44mph for 220 miles, and 44+8 = 52 mph for the next 208 miles.

 

Always a good idea to check your results.

 

If he drove 220 miles at 44mph, that means he drove for:

 

220 miles / 44 mph = 5 hours

 

If he drove 208 miles at 52mph, that means he drove for:

 

208 miles / 52 mph = 4 hours

 

5 + 4 = 9 hours, so the work checks out.

 

Hope this helps.

Answer 2

Not certain where the Pythagorean Theorem enters this problem.

 

Look at your units.  You are looking for an answer in miles per hour, and you are being asked about a segment of 220 miles.  Unfortunately, the only information you have concerning hours is the length of the entire trip.  But, if you divide miles by miles per hour that will give you a result in hour, which you can place in an equation with a known value.

 

220mi/xmph + 208mi/(x+8)mph = 9 hrs

(220x + 1760 + 208x)hrs /(x² + 8x) = 9 hrs

428x  = (9x² + 72x - 1751)

0 = 9x² - 356x - 1751

which will give us x=44mph (Use the Quadratic formula, the other result of -4.42 mph clearly will not work.)

 

check

220/44 + 208/(44+8) = 9

5 +208/52 = 5 + 4 = 9