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
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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(52781) (Show Source):
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.
