Solution:if a car traveled 5 km/h.Faster it would take one hour less to travel210 kilometer.What is the speed of car and what time does it take?
Let V be the actual speed, not the 5 km/h faster speed. Let T be the travel time (in hours) to go 210 km at speed V. You can write two equations.
V*T = 210
(V+5)(T-1) = 210
(V + 5)[(210/V) - 1] = 210
That can be converted to a quadratic equation, but I am going to try some numbers for V.
V = 30 km/h ( it works)
T = 7 hours
Let's solve this step by step:
Let's assume the speed of the car is x km/h.
Step 1: Determine the time it would take to travel 210 kilometers at a speed of x km/h:
Time = Distance / Speed
Time = 210 km / x km/h
Time = 210/x hours
Step 2: Determine the time it would take to travel 210 kilometers at a speed of (x+5) km/h:
Time = Distance / Speed
Time = 210 km / (x+5) km/h
Time = 210/(x+5) hours
Step 3: It is given that if the car traveled 5 km/h faster, it would take one hour less to travel 210 kilometers. So, we can set up the following equation:
210/x - 210/(x+5) = 1
Step 4: Solve the equation for x:
210(x+5) - 210x = 1(x)(x+5)
210x + 1050 - 210x = x^2 + 5x
1050 = x^2 + 5x
Step 5: Rearrange the equation to solve for x^2:
x^2 + 5x - 1050 = 0
Step 6: Solve for x using factoring, completing the square, or the quadratic formula:
(x + 35)(x - 30) = 0
x = -35 or x = 30
Since speed cannot be negative, we discard -35 km/h as a solution.
Therefore, the speed of the car is 30 km/h and it takes 210/30 = 7 hours to travel 210 kilometers.
To find the speed of the car and the time it takes to travel, we can use the following steps:
Step 1: Let's assume the original speed of the car is "x" km/h.
Step 2: So, if the car traveled at "x" km/h, it would take 210 km / x km/h = 210/x hours to travel the distance.
Step 3: Now, we are given that if the car traveled 5 km/h faster, it would take 1 hour less to travel the same distance of 210 km.
Step 4: So, the new speed of the car would be (x + 5) km/h.
Step 5: Using the new speed, it would take 210 km / (x + 5) km/h = (210/(x+5)) hours to travel the distance.
Step 6: As per the given information, the new time is 1 hour less than the original time. So, (210/(x+5)) = (210/x) - 1.
Step 7: Let's solve this equation to find the value of the original speed of the car "x".
210/(x+5) = (210/x) - 1
Step 8: To solve this equation, we can multiply each term by x(x + 5) to eliminate the denominators:
210x = 210(x + 5) - x(x + 5)
Step 9: Simplifying the equation:
210x = 210x + 1050 - x^2 - 5x
Step 10: Rearranging the terms:
0 = -x^2 - 5x + 1050
Step 11: We can solve this quadratic equation by factoring or applying the quadratic formula. After solving, we find that x = 30 or x = -35. However, since speed cannot be negative, we discard the -35 value.
Step 12: Therefore, the original speed of the car is 30 km/h.
To find the time it takes, substitute the speed value (x = 30 km/h) into the equation from Step 2:
Time = 210 km / 30 km/h = 7 hours.
So, the speed of the car is 30 km/h, and it takes 7 hours to travel 210 kilometers.