rainstorm question

Question

Greg drove at a constant speed in a rainstorm for 245
miles. He took a? break, and the rain stopped He then drove 240
miles at a speed that was 5
miles per hour faster than his previous speed. If he drove for 13
?hours, find the? car's speed for each part of the trip.

Answer 1

During storm: he drove at rate r for t hours;  245 = rt.

 

After storm: he drove at rate r+5 for 13-t hours;  240 = (r+5)(13-t).

 

So you have two equations & two unknowns.  Go from here!

Answer 2

Let's start by setting up an equation that expresses all the information we've been given in the word problem. We're given the total travel time (13 hours) as well as the distances for the two sections of the trip (245 and 240 miles). We can think of the total time as the sum of two section times, each of which is calculated as the quotient of distance and speed. That is:

 

13 = 245/x + 240/(x+5),

 

Where x is the original speed. Our task is to solve for x.

 

In order to do this, we convert the equation to a quadratic by multiplying by the denominators:

 

(13)(x)(x+5) = (245/x)(x)(x+5) + (240/(x+5))(x)(x+5)

 

13x² + 65x = 245x + 1225 + 240x

 

13x² - 420x - 1225 = 0

 

Factoring gives us

 

(13x + 35)(x - 35) = 0

 

Since we obviously aren't concerned with negative answers, the only relevant solution is x = 35.

 

So the speed for the first leg of the trip is 35 mph, and the speed for the second leg is x + 5 = 40 mph.