SOLUTION: Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken one hour less. Find the speed of his vehicle. What would the equation look like

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Question 17553: Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken one hour less. Find the speed of his vehicle. What would the equation look like for this word problem?
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
Distance=600miles,Speed=x mph
Time taken=(600/x)hours


Second case:
Distance=600miles,Speed=(x+20)mph
Time=(600/x+20)hours which we know is 1 hour less than the first case


So we get,
+%28600%2Fx%29+-+%28600%2F%28x%2B20%29%29+=+1+
[This is your required equation]
+%28600%28x%2B20%29-600x%29%2F%28x%28x%2B20%29%29+=+1+
+%28600x%2B12000-600x%29%2F%28x%5E2%2B20x%29+=+1+
+12000+=+x%5E2%2B20x+
+x%5E2%2B20x-12000+=+0+
This is a quadratic in x and can thus be solved as:
+x%5E2%2B20x-12000+=+0+
+%28x-100%29%28x%2B120%29+=+0+
So we get x=100 or -120 mph
This speed cannot be negative, thus x=100


Hope this helps,
prabhat