Devon travels 40 km to Edmonton by car, and then returns by bus. The average speed of the car is 20 km/h greater than the average speed of the bus. If Devon's total travel time is 54 min, what is the average speed of the bus?
Let's assume the average speed of the bus is x km/h.
Since the average speed of the car is 20 km/h greater than the average speed of the bus, the average speed of the car is (x+20) km/h.
Devon travels 40 km to Edmonton by car and 40 km back by bus, so the total distance covered is 2 * 40 = 80 km.
We know that speed = distance / time. Let's calculate the time it takes to travel 40 km by car:
Time taken by car = Distance / Speed
= 40 km / (x+20) km/h
Similarly, the time it takes to travel 40 km by bus would be:
Time taken by bus = Distance / Speed
= 40 km / x km/h
The total travel time is given as 54 minutes, which is equal to 54/60 = 0.9 hours. Therefore, we can write the equation:
Time taken by car + Time taken by bus = 0.9 hours
Substituting the values, we have:
40/(x+20) + 40/x = 0.9
To solve this equation, we can cross-multiply:
40*x + 40*(x+20) = 0.9 * (x+20) * x
Simplifying further:
40x + 40x + 800 = 0.9x^2 + 18x
Bringing all terms to one side, we get a quadratic equation:
0.9x^2 + 18x - 80x - 800 = 0
0.9x^2 - 62x - 800 = 0
Now we can solve this quadratic equation for x using factoring, completing the square, or the quadratic formula.
Solving this quadratic equation, we find two possible solutions for x: x = -6.667 and x = 15.555.
Since speed cannot be negative, the average speed of the bus is approximately 15.555 km/h.
To solve this problem, we need to set up equations based on the given information.
Let's assume that the average speed of the bus is x km/h. Since the average speed of the car is 20 km/h greater than that, the average speed of the car would be (x + 20) km/h.
We know that time = distance / speed. Therefore, we can set up two equations based on the distances traveled by car and by bus:
Time taken by car = Distance / Speed of the car
Time taken by bus = Distance / Speed of the bus
Since the distance traveled is the same in both directions (from Edmonton to the destination and back), we can set up the following equation:
Time taken by car + Time taken by bus = Total travel time
Converting the total travel time from minutes to hours:
Total travel time = 54 minutes / 60 minutes/hour = 0.9 hours
Now let's substitute the equations we set up earlier into the equation for total travel time:
40 km / (x + 20 km/h) + 40 km / x = 0.9 hours
To solve this equation, we can get rid of the denominators by multiplying both sides of the equation by x(x + 20):
40x + 40(x + 20) = 0.9x(x + 20)
Simplifying this equation:
40x + 40x + 800 = 0.9x^2 + 18x
Combining like terms and rearranging to set the equation to zero:
0.9x^2 - 62x - 800 = 0
Now you can solve this quadratic equation using factoring, completing the square, or the quadratic formula to find the value(s) of x. The positive value(s) of x will represent the average speed of the bus.
Once you find the value(s) of x, you will have the average speed(s) of the bus.
Help needed urgently. Please Help.
since time = distance/speed, if the bus's speed is x, then
40/x + 40/(x+20) = 9/10
Now just find x, and x+20