A car travels 20 kph faster than a truck. The car covers 350 km in two hours less than the time it takes the truck to travel the same distance. What is the speed of the car? How about the truck?
If the truck has speed x, then the car has speed x+20
since time = distance/speed,
350/(x+20) = 350/x - 2
Now just solve for x, and figure x+20
But the x would be zero! Help!!
A car travels 20 kph faster than a truck. The car covers 350 km in two hours less than the time it takes the truck to travel the same distance. What is the speed of the car? How about the truck?
To solve this problem, we can use a system of equations. Let's assume the speed of the truck is represented by "t" kph. Since the car is traveling 20 kph faster than the truck, the speed of the car would be "t + 20" kph.
Now, let's use the given information and set up the equations:
Equation 1: The car covers 350 km in two hours less than the time it takes the truck to travel the same distance. We can represent this as:
350/(t + 20) = 350/t - 2
Equation 2: The distance traveled by both the car and the truck is the same (350 km):
350 = t * (350/t) = 350
Now, let's simplify Equation 1 by multiplying both sides by (t + 20) and distribute:
350 = 350 - 2(t + 20)
Simplify further:
350 = 350 - 2t - 40
Combine like terms:
2t = 40
Divide both sides by 2:
t = 20
Therefore, the speed of the truck is 20 kph.
Now, let's substitute this value back into Equation 2 to find the speed of the car:
350 = (20 + 20)
Simplify:
350 = 40
Therefore, the speed of the car is 40 kph.
In conclusion, the speed of the car is 40 kph, and the speed of the truck is 20 kph.