SOLUTION: Greg drove at a constant speed in a rainstorm for 288 miles. He took a break, and the rain stopped He then drove 160 miles at a speed that was 4 miles per hour faster than

Question 1088337: Greg drove at a constant speed in a rainstorm for 288 miles. He took a break, and the rain stopped He then drove 160 miles at a speed that was 4 miles per hour faster than his previous speed. If he drove for 12hours, find the car's speed for each part of the trip.
Answer by ikleyn(52783) (Show Source): You can put this solution on YOUR website!
.

Let x be the Greg's rate in a rainstorm, in mph.

Then his rate after rain stopped was (x+4) mph.


The time Greg drove at the rain was  hours.

The time Greg drove after rain stopped was .


The total time Greg drove was   + .

And the condition says it was 12 hours in total.


It gives you an equation

 +  = 12.


To solve it, multiply both sides by x*(x+12). You will get

288*(x+4) + 160x = 12x*(x+4).


Simplify and solve for x:

12x^2 - 400x - 288*4 = 0  ====>  3x^2 - 100x - 288 = 0 ====>

 =  = .


Only positive of the two roots make sense: x =  = 36.


Answer.  Greg's rate at the rain  was 36 mph.  His rate after rain stopped was 36+4 = 40 mph.

Solved.

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SOLUTION: Greg drove at a constant speed in a rainstorm for 288 miles. He took a&#8203; break, and the rain stopped He then drove 160 miles at a speed that was 4 miles per hour faster than

SOLUTION: Greg drove at a constant speed in a rainstorm for 288 miles. He took a break, and the rain stopped He then drove 160 miles at a speed that was 4 miles per hour faster than