Another math word problem..help pls,,?

Question

a car travels 15 mph faster than a truck and goes a distance of 220 miles in one and one-half hour less time than required by the truck to travel the same distance. find the speed of each vehicle.

thank you :)

Answer 1

If x and x+15 are the speeds,

220/x -220/(x+15) = 3/2.

so 6600 = 3x(x+15)

Means x(x+15) = 2200 so x = 40 and x+15 = 55.

What is mph by the way? Miles per hours? who still uses this out dated unit?

Answer 2

speed of truck is x

speed of car is x+15

220/(x+15) + 1.5 = 220/(x)

220x +1.5 = 220(x+15)

220x +1.5(x^2+15x)= 220x + 3300

1.5x^2+22.5x-3300=0

factor out quadratic

x= 40 x= -55 speed can't be negative so -55mph is invalid

speed of truck is 40 mph and speed of car is 55 mph

hope this helps  

Answer 3

Travel time of truck (y):

xy = 220

y = 220/x

(x + 15)(y - 1.5) = 220

y - 1.5 = 220/(x + 15)

y = (220/[x + 15]) + 1.5

Speed of truck (x):

220/x = (220/[x + 15]) + 1.5

220/x = (220 + 1.5x + 22.5)/(x + 15)

220/x = (242.5 + 1.5x)/(x + 15)

220(x + 15) = x(242.5 + 1.5x)

220x + 3,300 = 242.5x + 1.5x²

440x + 6,600 = 485x + 3x²

3x² + 45x = 6,600

x² + 15x = 2,200

x² + 15/2x = 2,200 + (15/2)²

x² + 15/2x = 8,800/4 + 225/4

(x + 15/2)² = 9,025/4

x + 15/2 = 95/2

x = 80/2 or 40

Speed of the car:

= 40 + 15

= 55

Answer: truck, 40 mph; car, 55 mph

Proof (equal distance, different speeds and travel time):

Travel time of truck:

= 220 mi/40 mph

= 5.5 hrs

Distance traveled by truck = Distance traveled by car

5.5 hrs(40 mph) = (5.5 - 1.5 hrs)(40 + 15 mph)

220 mi = 4 hrs(55 mph)

220 mi = 220 mi