SOLUTION: Mr. Martin traveled to a city 150 miles from his home to attend a meeting. Due to car trouble, his average speed returning was 10 mph less than his speed going. If the total time

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Question 1008675: Mr. Martin traveled to a city 150 miles from his home to attend a meeting. Due to car trouble, his average speed returning was 10 mph less than his speed going. If the total time for the round trip was 5 hours, at what rate of speed did he travel to the city? (Round your answer to the nearest tenth.)
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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R=rate going to other city
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150mi%2FR%2B150mi%2F%28R-10%29=5
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%28%28150mi%29%28R-10%29%2B%28150mi%29%28R%29%29%2F%28R%29%28R-10%29=5
150R-1500%2B150R=5%28R%29%28R-10%29
300R-1500=5R%5E2-50R
0=5R%5E2-350R%2B1500
0=R%5E2-70R%2B300
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aR%5E2%2BbR%2Bc=0 (in our case 1R%5E2%2B-70R%2B300+=+0) has the following solutons:

R%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-70%29%5E2-4%2A1%2A300=3700.

Discriminant d=3700 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--70%2B-sqrt%28+3700+%29%29%2F2%5Ca.

R%5B1%5D+=+%28-%28-70%29%2Bsqrt%28+3700+%29%29%2F2%5C1+=+65.4138126514911
R%5B2%5D+=+%28-%28-70%29-sqrt%28+3700+%29%29%2F2%5C1+=+4.5861873485089

Quadratic expression 1R%5E2%2B-70R%2B300 can be factored:
1R%5E2%2B-70R%2B300+=+1%28R-65.4138126514911%29%2A%28R-4.5861873485089%29
Again, the answer is: 65.4138126514911, 4.5861873485089. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-70%2Ax%2B300+%29

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Since 4.5 does not work (returning was 10 mph less would
result in negative speed), his rate going to the city was
65.4 mph.
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ANSWER: His rate traveling to the city was 65.4 mph
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CHECK:
150 mi/65.4mph+150mi/55.4mph = 5 hours
2.29 hours + 2.71 hours = 5 hours
5 hours = 5 hours
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