SOLUTION: Alexa makes a journey of 430km, traveling 160km by bus and 270km by car. If the car averages 10km/h faster than the bus and the whole journey takes 5 hours, what is the speed of

Question 1155618: Alexa makes a journey of 430km, traveling 160km by bus and 270km by car. If the car
averages 10km/h faster than the bus and the whole journey takes 5 hours, what is the
speed of the car?
Found 3 solutions by ikleyn, mananth, MathTherapy:
Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.

Write the "time equation" + = 5 hours, where x is the unknown speed of the car. And then solve it. ANSWER (which can be obtained mentally) is x= 90 kilometers per hour.

Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
Alexa makes a journey of 430km, traveling 160km by bus and 270km by car. If the car
averages 10km/h faster than the bus and the whole journey takes 5 hours, what is the
Time by bus + time by car = 5

Multiply by LCD
160 (x + 10 )+ 270 x = 5 x(x+ 10 )
160 x + 1600 ,+ 270 * x = 5 x^2 + 50
-5 X^2+ 380 x + 1600 = 0
Find the roots of the equation by quadratic formula

a= -5 ,b= 380 ,c= 1600 -33.75
b^2-4ac= 176400
b^2-4ac= 144400 - -32000
b^2-4ac= 176400 = 420

x1=( -380 + 420 )/ -10 29.8258
x1= -4
x2=( -380 -420 ) / -10 415.0943156
x2= 80
Ignore negative value
x = 80 mph Bus speed
90 mph= Car speed

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
Alexa makes a journey of 430km, traveling 160km by bus and 270km by car. If the car
averages 10km/h faster than the bus and the whole journey takes 5 hours, what is the
speed of the car?

Once again, this can be done MUCH, MUCH simpler! No need to use the quadratic equation formula!
Let the car's speed be S
Then the bus' speed = S - 10
We then get the following TIME equation:
------ Factoring out GCF, 5, in numerator
32S + 54(S - 10) = S(S - 10) -------- Multiplying by LCD, S(S - 10)

(S - 90)(S - 6) = 0
S, or speed of car = OR S = 6 (ignore)
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