Question

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

Answer 1

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

Answer 2

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.
`(280)/(x-2) -(300)/(x) =20`

cancel 20 on both sides and simplify

`(14)/(x-2) -(15)/(x) =1\\14x-15x+30 = x^2-2x\\x^2-x-30=-0\\x=6`

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.