SOLUTION: Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.

Algebra ->  Rational-functions -> SOLUTION: Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.       Log On


   

Question 200501: Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Remember, the distance-rate-time formula is

d=rt

Since he "traveled 600 miles at a certain speed", this means that the first equation is 600=rt

The statemtent "Had gone 20mph faster, the trip would have taken 1 hour less", tells us that the next equation is 600=%28r%2B20%29%28t-1%29


600=rt Start with the first equation.


600%2Fr=t Divide both sides by r.


t=600%2Fr Rearrange the equation


600=%28r%2B20%29%28t-1%29 Move onto the second equation.


600=%28r%2B20%29%28600%2Fr-1%29 Plug in t=600%2Fr


600=600-r%2B12000%2Fr-20 FOIL


600r=600r-r%5E2%2B12000-20r Multiply every term by the LCD r to clear the fractions.


0=600r-r%5E2%2B12000-20r-600r Subtract 600r from both sides.


0=-r%5E2-20r%2B12000 Combine and rearrange the terms.


Let's use the quadratic formula to solve for r


r+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


r+=+%28-%28-20%29+%2B-+sqrt%28+%28-20%29%5E2-4%28-1%29%2812000%29+%29%29%2F%282%28-1%29%29 Plug in a=-1, b=-20, and c=12000


r+=+%2820+%2B-+sqrt%28+%28-20%29%5E2-4%28-1%29%2812000%29+%29%29%2F%282%28-1%29%29 Negate -20 to get 20.


r+=+%2820+%2B-+sqrt%28+400-4%28-1%29%2812000%29+%29%29%2F%282%28-1%29%29 Square -20 to get 400.


r+=+%2820+%2B-+sqrt%28+400--48000+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%2812000%29 to get -48000


r+=+%2820+%2B-+sqrt%28+400%2B48000+%29%29%2F%282%28-1%29%29 Rewrite sqrt%28400--48000%29 as sqrt%28400%2B48000%29


r+=+%2820+%2B-+sqrt%28+48400+%29%29%2F%282%28-1%29%29 Add 400 to 48000 to get 48400


r+=+%2820+%2B-+sqrt%28+48400+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


r+=+%2820+%2B-+220%29%2F%28-2%29 Take the square root of 48400 to get 220.


r+=+%2820+%2B+220%29%2F%28-2%29 or r+=+%2820+-+220%29%2F%28-2%29 Break up the expression.


r+=+%28240%29%2F%28-2%29 or r+=++%28-200%29%2F%28-2%29 Combine like terms.


r+=+-120 or r+=+100 Simplify.


Since a negative speed doesn't make any sense, this means that the only solution is r+=+100


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Answer:


So the speed of his vehicle is 100 mph



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