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A car travels between 2 towns 60 miles apart at an average speed of V mph. If the average speed had been 10mph more the car would have taken 30 minutes less.
Write an equation for v and hence find V

Respuesta :

Medunno13

Answer:

V = 30

Step-by-step explanation:

distance = (speed)(time)

We know that originally, the car traveled for 60/V hours.

So,

[tex]60=\left(\frac{60}{V}-\frac{1}{2} \right)(V+10) \\ \\ 60=60+\frac{600}{V}-\frac{V}{2}-5 \\ \\ 0=\frac{600}{V}-\frac{V}{2}-5 \\ \\ 0=1200-V^2 -10V \\ \\ V^2 +10V-1200=0 \\ \\ (V+40)(V-30)=0 \\ \\ V=-40, 30[/tex]

Speed cannot be negative, so V = 30.

adioabiola

The equation for the speed V of the car can be determined by determining the distance equation as a function of time and velocity as follows; v² +10v -1200 = 0 and the value of V is; 30mph.

What is the speed of the car?

Distance = 60 miles.

Hence, since the task content says; If the average speed had been 10mph more the car would have taken 30 minutes less, then; we have;

60 = ((60/v) - 1/2)(v +10)

Hence, upon simplification; we have;

v² +10v -1200 = 0

(v+40) (v-30) = 0

v = -40 OR v = 30.

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