Savanna's truck takes two hours longer to travel 300 miles then Tony's car takes to travel 280 miles Tony's car travels 20 mph faster than savanna's truck find the rate and time

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

$32,660

step-by-step explanation: