SOLUTION: A man covers distance of 120 km from town A to Town B at an average speed x km/h. If he increased his average speed by 1 km/h he would saved 30 minutes. What is his average speed?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A man covers distance of 120 km from town A to Town B at an average speed x km/h. If he increased his average speed by 1 km/h he would saved 30 minutes. What is his average speed?      Log On


   

Question 874687: A man covers distance of 120 km from town A to Town B at an average speed x km/h. If he increased his average speed by 1 km/h he would saved 30 minutes. What is his average speed?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
CONDITION________speed________time_______distance
Did_______________x____________t_________120=xt
If_______________x+1__________t-1/2______120=%28x%2B2%29%28t-1%2F2%29

Both x and t can be solved. See that a substitution will be possible using the "did" equation.

The "If" equation,
xt%2B2t-x%2F2-1=120
xt%2B2t-x%2F2-1=xt
2t-x%2F2-1=0
4t-x-2=0
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Again substitute using t=120%2Fx.
480%2Fx-x-2=0
480-x%5E2-2x=0
-x%5E2-2x%2B480=0
highlight%28x%5E2%2B2x-480=0%29.
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Check discriminant. 4+4*480=1924.
481 is a prime number.
4(481) is discriminant.
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x=%28-2%2Bsqrt%284%2A481%29%29%2F2
x=%28-2%2B2sqrt%28481%29%29%2F2
highlight%28x=-1%2Bsqrt%28481%29%29