Respuesta :
Answer:
Step-by-step explanation:
Let x be the speed of Savanna's truck. ?Time taken to travel 300 miles = 300/x
Tony's car speed = distance/time 280/(x-2)
Given that Tony is faster than Savannaby 20 mph
i.e. [tex]\frac{280}{x-2} -\frac{300}{x} =20[/tex]
cancel 20 on both sides and simplify
[tex]\frac{14}{x-2} -\frac{15}{x} =1\\14x-15x+30 = x^2-2x\\x^2-x-30=-0\\x=6[/tex]
x cannot be negative
so x = 6 hours
i.e. Speed of Savanna is 50 mph and speed of
Tony is 70 mph
Time taken for Savanna to travel 300 miles is 6 hrs while for Tony to travel 280 miles is 4 hours.
Answer:
Step-by-step explanation:
Let x represent the speed of Savanna's truck .
If Tony's car travels 20 mph faster than savanna's truck, it means that the speed of Tony's car is (x + 20) mph
Time = distance /speed.
Time taken for Tony's car to travel 280 miles is 280/(x + 20)
Time taken for savanna's truck to travel 300 miles is 300/x
Since savanna's time = Tony's time + 2 hours, then
300/x = 280/(x + 20) + 2
Multiplying through by x(x + 20), it becomes
300(x + 20) = 280x + 2x(x + 20)
300x + 6000 = 280x + 2x² + 40x
2x² + 40x + 280x - 300x - 6000 = 0
2x² + 20x - 6000 = 0
Dividing through by 2, it becomes
x² + 10x - 3000 = 0
x² + 60x - 50x - 3000 = 0
x(x + 60) - 50(x + 60) = 0
x - 50 = 0 or x + 60 = 0
x = 50 or x = - 60
Since the speed cannot be negative, then
x = 50 mph
Savanna's speed is 50 mph
Savanna's time is 300/50 = 6 hours
Tony's speed is 50 + 20 = 70mph
Tony's time is 280/70 = 4 hours
