Answer: x = 50
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Step-by-step explanation
distance = rate*time
d = r*t
150 = x*t
t = 150/x
If his speed is x km per hour, then he will drive for 150/x hours.
d = r*t
150 = (x+10)*t
t = 150/(x+10)
If he increases the speed to (x+10) km per hour, then he drives for 150/(x+10) hours.
At this faster speed, he arrives 30 min = 30/60 = 1/2 an hour sooner.
The time duration gap between 150/(x+10) and 150/x is 1/2 an hour.
slowerTime - fasterTime = 1/2 hour
150/x - 150/(x+10) = 1/2
2x(x+10) * [ 150/x - 150/(x+10) ] = 2x(x+10)*(1/2)
300(x+10) - 300x = x(x+10)
300x+3000 - 300x = x^2+10x
3000 = x^2+10x
x^2 + 10x - 3000 = 0
(x+60)(x-50) = 0
x+60 = 0 or x-50 = 0
x = -60 or x = 50
Ignore the negative solution. A negative speed doesn't make sense in this context. An alternative approach is to use the quadratic formula.
He traveled at a speed of 50 km per hour
It takes him 150/50 = 3 hours at this starting speed.
Going 10 km per hour faster means he now travels at 50+10 = 60 km per hour. He would take 150/60 = 2.5 hours which is 0.5 = 1/2 hour shorter compared to the 3 hours found earlier. This confirms the answer.